Even if you can't sew, it's fairly easy to learn how to make a caveman costume, especially if you're not trying to construct a Neolithic face. You can be as simple or elaborate as you wish - you don't even have to carry a club.
How to Make a Caveman Costume: Basic
If you're seeking a quick and cheap costume idea, a caveman can do the trick nicely. To create this suit, any brown fabric will do, although dyed muslin or burlap would look the best on short notice if you don't want to buy faux fur. For an indoor event or a warm night, you can forgo a shirt altogether or wear a tank top and shorts and drape the fabric around you like a toga. You want the costume to hang no longer than knee-length. Depending on your comfort level, it can also be much shorter. Knot the fabric over one shoulder and hang the rest around you, holding it in place with safety pins or more knots. Use some dark makeup to make your face dirty, wear sandals or go barefoot and you're done.
More Elaborate Costumes
Learning how to make a caveman costume that really rocks the cave is still easy. Again, while fake fur is the most classic option, you can still use dyed burlap or muslin - cave folk were not necessarily always dressed in the latest fur and may have mixed it up with other skins. So long as your outfit looks rough and lived-in, you'll pass.
Your choices for the shape of the costume vary. Modesty may dictate something more like a tunic. Even if your torso is not something you usually display, you may find that doing so makes the costume even funnier (cavemen outfits are naturally amusing), and that's worth it. In that case, the over the shoulder look might appeal. A man can also just drape "skins" around his hips and accessorize his look with bone necklaces. If you don't have a hairy chest but would like to for a night, you can achieve as much either by buying a T-shirt with a hairy chest drawn on or by turning a plain shirt into a hairy one with a fabric marker. It will look silly, but that's part of the fun.
If you really want to go town, a makeup artist can help set you up with actual fake body hair, but that is only for a serious costume event.
Sewing When You Can't Sew
A caveman outfit is one of the easiest to create if you can't sew, because it doesn't matter how sloppy it looks. The most sewing involved will be for the tunic version. If you're concerned about fit, make a muslin version first and use it as a model to guide you. You just need to make a long, shapeless, sleeveless top of two even pieces, sewn up each side. Sewing through fake fur can be hard on the hand or a machine - a special needle is required. If you're short on time and patience, large safety pins can do the trick as well. At the top, however, you really want to sew the pieces together because safety pins resting on your shoulders will be very uncomfortable. Or, if you like, you can cut the shoulder straps extra long and tie the ends together - this will look very caveman-like.
Accessories may sound silly when you're talking about how to make a caveman costume, but a few props always add interest. In this case, you'll want fake bones and teeth. You can make teeth and bones out of clay bought at the craft store and string them together with leather string to make a necklace. You can also wind the bones inside the shoulder strap to make them look like pins.
The classic club is the hardest thing to make, although you can add some padding to a baseball bat and paint it brown. You can also go without and act as a caveman who simply gathers.