Can't use the usual filters, or don't have any old ones laying around? That's OK—there are loads of solutions that are completely from scratch.
Cans are strong, cheap—and many mysteriously enough are perfect fits for sliding over the lens barrel. Think sizes anywhere between Pringle cans to Cambell's Chicken Noodle Soup—whatever fits your particular lens barrel. This'll require a strong cutting utensil that can safely cut through thin metal (and maybe some tape for those sharp edges), but once you have it cut to fit, this filter mount isn't likely to break. If you're using unlined metal, there's a risk of scratching the lens barrel. If this displeases you, it's pretty easy to line a tin can with paper.
Of course, it doesn't have to be a can either. Old toilet paper or paper towel rolls, empty tape rolls, just think about any circular cylindrical object you might have laying around that might fit your camera. If you're using paper products, you'll want to both waterproof and stiffen the product so that it can work under even extreme conditions. An easy way to do this is by wrapping the entire roll with electrical tape, which also adds a nice professional black finish to the filter.
If you don't have anything laying immediately around the house, it's just a trip to the supermarket away. Pringle cans, paper towel rolls, there are many cheap and useful products that may be reused for filters. Just take along your camera and see what fits!
With this method, it's a good idea to color the inside of the filter mount black with a Sharpie or some other permanent black marker. This will ensure that the light colouring of the inside of the cylinder will not end up discoloring your photo in any way.
A disadvantage to these types of filters is that it is difficult to attach multiple filters in this manner. It can also be a bit unwieldy if the filter isn't a perfect fit over your lens. It's recommended that filters that will be getting a heavy workout use the previous methods—something that will physically screw onto your camera—be used if possible for, say, that polarized filter you use all the time.