A tiny gauss rifle built from only a few strong magnets. (It's not a coil or rail gun since its got no electromagnets, so I went with gauss rifle.)
Step 1: Acquire Magnets
You will want some strong rare earth (Neodymium) magnets of two sizes. The larger size should be a ring magnet. The smaller magnet can be a ring or cylinder, and should fit snuggly into the first one. You can actually stack together several magnets, but single cylinders might work better.
I get my rare earth magnets from http://www.kjmagnetics.com/
Step 2: Arrange Magnets
Place the smaller magnet(s) end to end with the larger ring magnet(s). It should attract end to end but be off center as shown. If you attempt to join the magnets at the wrong ends, they will repel. (Although if you try really hard you can get the smaller ones stuck in the bigger. That's not what you want to do.)
Step 3: Load Rifle
Load the rifle by forcing the smaller magnet(s) into the larger. It will go in, but may take some work. Ideally you'll have some of the smaller magnet(s) sticking out both ends, as shown. This is the locked and loaded (and potentially dangerous) state. Be careful.
You'll want to make sure the inner magnet(s) fit into the outer. It should be a snug fit, not loose. It should also not be so tight that it can't shoot back out.
Step 4: Fire!
Holding the rifle by its sides, point one flat end at a nice, soft, non-living target. The Neodymium magnets are fragile and will break, plus they can hurt people so be really careful.
Firmly push the inner magnet(s) into the outer and it should pop out the other end with greater force.