Different Fursuit Styles

"Stage" Makeup

(See Sample Pictures)
Although makeup alone does not, perhaps, qualify as a fursuit, makeup techniques are still valuable talents for a costumer. It is not uncommon to create a suit to cover the body and simply use makeup for the face. This combination has the advantages of not inhibiting your sight or eating ability while also keeping you cooler; it's disadvantages are a lack of realism (if realism is your goal; symbolically it can still be terribly effective) and the preparation time (each and every time).
The costuming aspect of fursuiting descended from stage costuming, so it is probably natural that people involved in fursuiting would also have some interest in stage makeup. The talents of makeup application still find their uses. However, these pages are more oriented towards costume construction, so no additional information about makeup will be included here.

Sewn Suits ("Mascot Style")

(See Sample Pictures)
Sewn suits are perhaps the most familar style of fursuit. These often take the form of zippered suits or "jumpers", which are sewn from synthetic fur material. This style of fursuit is what is commonly used for mascots, rental costumes, and most mass- produced costumes.
This style of costuming has several notable advantages. First, the costumes are (relatively) quick to make; making a sewn bodysuit involves determining a pattern (possibly the hardest part, especially for first-timers and those inexperienced at sewing), cutting the fur, and then sewing the fur together without putting a piece in with the nap going the wrong way. :) I have been told that such projects get easier with practice, however. Note that, although they might be faster in assembly, I am definitely not saying that they are less artistic or less effective as costumes.
Another advantage is that such costumes are washable, presuming the fur is washable. Cheap synthetic fur ("FunFur" seems to be the predominant brand and, as with facial tissues ("Kleenex"), the brand name is synonymous with the product) is washable with little change to the fiber characteristics. Those with more experience tell me that washing it with a little Woolite will get the fur quite clean; the color does not fade from washing (from sunlight, sometimes), though the texture of the fur becomes a little rougher after the first washing.
Although sewn suits have many strong advantages, they are not the ultimate fursuit solution. Their main disadvantags is that they are not realistic (if your goal is to protray an animal or near-animal, particularly). They are designed as clothing on a human form, and this is their limitation. However, this can be largely overcome by using padded inserts. Adding shaped pieces of foam, either individual pads or an undersuit with the padding sewn to it, can help to redesign the perceived body shape. This style of sewn suit requires more work, but is perhaps one of the most effective methods of creating a character costume.
Sewn suits are matched with many different methods of head construction. Most often, from what I've seen, they are used with foam or fiberglass heads. They are also used with cast latex masks (often the case on rental costumes) and prosthetics or makeup. The paws are often sewn from fur, although latex appendages are common for "monster" costumes.

Foam [Buildup] Bodysuits

(See Sample Pictures)
This is a more complex form of fursuit, usually selected for better definition of body shape. These fursuits are created by attaching carved foam to a unitard or close-fitting undersuit; this "foam buildup" creates a new shape on top of the wearer's body. A layer of fur is then attached to the foam to complete the suit.
This style of fursuit design's advantage is that it may produce much more realistic/inhuman body shapes. Whereas a sewn suit must be hung on a human frame, this style of suit uses foam padding attached to a skin-tight suit to effectively redefine the surface beneath the fur. If properly designed, the movement of the foam can even give the illusion of muscles beneath a layer of fur. Usually, the fur is attached directly to the foam padding, using hot glue; it is also possible to sew the outer fur layer so that it fits tightly over the foam layer. This second technique is much more labor intensive because it combines the difficulties of foam-buildup and sewn-suit design, but it allows the fur to slide a little over the foam, giving the illusion of an animal's hide shifting over a muscle layer.
There are many disadvantages which must be accepted in exchange for this newfound realism. First, this style of costume is, from all I hear, one of the more difficult approaches to fursuiting. Secondly, since the costume is skin-tight, it fits only one person (or people of almost identical stature). Also, because the suit is worn against the skin, this style of fursuit is very hot.
So is this style worthwhile? It all depends on the visual effect you want to achieve with the costume. I chose this style for my first fursuit project; it was difficult, but I was pleased with the results.

Foam, Wire, and Fiberglass Heads

(See Pictures for "Sewn Suits" until I can find better!)
Thus far, the styles have been focused on the body of the costume. Yet the head is one of the most important, and difficult, parts of a fursuit. The initial visual impact of the head is one of the major factors in the persona of a fursuit.
One of the most prolific styles for mascots and "character" costumes is the foam/wire/fiberglass head. These three construction methods are similar in style, but differ in the materials used. The basic idea is to create a hollow shell, the fursuit's head, which can be easily donned by lowering it over the head of the wearer. Typically, the costume head rests on the shoulder's of the wearer.
The head may be constructed in a variety of ways. The "foam" method uses upholstery foam carved into the shape of the fursuit head. A hollow is carved into the middle that is large enough to accomodate the wearer's head. The "wire" method involves creating a framework of brass wires to shape the head; the fur is then sewn down to the wires, over a layer of batting. The "fiberglass" technique is the most complex and detailed; it involves creating a sculpture of the character head, taking a negative of this, then creating a layer of fiberglass inside this negative (fiberglass materials are available at reasonable prices at many hobby stores for use by model airplane enthusiasts). Fur (or paint) can then be applied directly to the fiberglass.
Each of these styles produces heads with approximately the same visual appearance (excepting painted fiberglass). These heads are generally large (not a problem for 'toon characters), have wide or non-existant necks (since the wearer's head must enter the costume head through the neck hole), have fake eyes (since the eyes of the wearer would usually appear too far back in the head), and have fixed expressions (with some exceptions). These head styles are relatively easy to make and are very easy to take on/off. As for the perpetual problem of heat, they are not too terrible; since the heads are oversized and have internal structure, though, fans may often be mounted in the head to keep the wearer cooler.

Latex Heads/Appendages

(See Sample Pictures)
One technique that has found many uses in costuming is cast-latex sculpture. This technique uses latex, a synthetic rubber compound in its liquid form, to recreate the inside surface of a negative mold (i.e. a hollow). Once dried, the latex layer from the inside of the mold forms a somewhat-pliable and lightweight surface.
The cast-latex process is most commonly used to create masks for the faces of character (and "monster") costumes. This includes most of the masks commonly seen at Halloween stores. Creating such a mask involves first sculpting a clay positive of the outside surface of the mask; this may include all or part of the head and may have any amount of detail desired. Plaster or some other casting compound is then used to create a negative of the sculpture. Liquid latex is then poured into this plaster cavity; the latex that contacts the plaster surface will dry, and the excess liquid latex can be poured out of the mold for reuse later. The resultant skin may be peeled from the negative when fully dry; this is the mask.
This process is relatively simple, although a bit time-consuming. This may partially explain the popularity of cast-latex. Additionally, the latex skin can reflect fine details (almost down to the level of skin texture, given the right casting materials) which makes it ideal for non-furred masks. Finally, the product is light- weight and easy to take on/off.
Cast-latex is often used for hands/paws on costumes, as well. It can hold any shape, however bizarre, as long as it's not too heavy (the latex is only so strong as a self-supporting structure). If a furred surface is desired, the fur may be glued directly to the latex using a surface adhesive or rubber cement. The only disadvantage to using cast-latex is the time and materials involved (especially if you're only making a single item) and the heat from wearing it (latex traps heat and sweat quite effectively).
Also note that if the latex is to be a non-furred surface, it needs to be painted. This will require an airbrush and talent (only one of which may be purchased at the local art store:).

Prosthetic Effects

(See Sample Pictures)
Prosthetics are a special technique developed as part of stage and FX makeup. It involves creating an "appliance", a specially molded piece of foam rubber or other soft material, which is glued directly to the face/body of the wearer. Prosthetic effects are one of the most complex techniques used in costuming, but the results can be amazingly realistic.
Prosthetics are generally used to augment a person's face. This technique is most useful if the desired appearance is not too far removed from the natural shape of the face; this is not a requirement, however. The larger/thicker the appliance is, though, the less realistically the movements of the underlying facial muscles will translate through the appliance. On thin appliances, the movements of the wearer are clearly matched by the movements of the appliance's "skin", which is what allows prosthetics to yield such powerful visual impact.
Creating a prosthetic appliance is a long process. The appliance must be developed to specifically fit the face/body of the wearer, so the first step is to make a lifecast of the person. A lifecast is a plaster or Ultracal duplicate of the area of the wearer's body on which the appliance is to be worn; the creation of a lifecast involves coating the intended wearer with algenate, then a plaster outer layer, then removing this from the wearer and filling it with casting compound. More details on this process will be added soon, in case you are interested in giving it a try.
The shape of the appliance must then be sculpted on the lifecast in oil-based clay; this produces an augmented positive. This is then cast in plaster (producing an augmented negative and usually ruining the clay sculpture). The space formed when the lifecast and augmented negative are held back together is the shape of the prosthetic appliance. Using these together as a mold, it is thus possible to fill the volume with expanding-foam or whipped latex. After a period of drying, the mold can be separated and the appliance removed.
Above and beyond this tedius creation process, the appliance still needs to be painted and augmented with any necessary pieces of fur (which usually have to be hand-punched).
Although this is clearly not the easiest route for a fursuiter to take, prosthetics are often used by those seeking realism. Their only other disadvantages are that they are fitted to only one wearer (this is also a problem with foam-unitard body suits, though, with which prosthetics are often combined) and that they involve applying makeup to the body (somewhat time-consuming, though rarely longer than an hour with a single-piece prosthetic).

Further Miscellany

There are many other materials and techniques used in fursuiting. For example, mask underskulls may be created with papier mache or vacuu-formed plastic. The techniques covered above are some of the most commonly used styles, but they should not be thought of as limitations. Fursuit creation is a highly individualzed and distinctive art. It would be impossible to list all of the materials that one might use. The only true test of a fursuit is its final appearance.