A simple, low-tech way to have fun with gravity. Often employed by rock climbers because they already have the gear and the knowhow, but anyone can do it, and if you exercise a modicum of common sense, you can live to tell the tale.
Your location should be chosen for a dramatic and unobstructed fall line, an excellent view, and proximity to medical help. Most folks set the top anchor high in a tree and the low anchor at the base of another tree, but I've done it off of railroad bridges, rock faces and across gullies as well.
Make a loop of nylon webbing by tying the ends together with a water knot, then double the loop and run that around your top anchor point and fasten *all four* loop-ends with either a locking carabiner or two regular 'biners with gates opposed. Needless to say(?), your top anchor should be set in such a way that flipping or bouncing of the rope will not unseat it, and you should check it under tension to make sure the webbing is not rubbing against any sharp edges.
Repeat with another loop of webbing at your bottom anchor point. A key point to remember about your low anchor is that as you approach it you will be traveling almost horizontally, and that you'll slide along the ground further than you might think at first. Allow enough distance for friction to stop you, and do not fasten the anchor more than a few inches above the ground unless you *want* to slam into it.
Put a figure eight knot in the end of your rope and clip it to the carabiner(s) of the the top anchor. Unless you have placed your anchors in such a way as to use exactly the full length of your rope, you'll need to make a bight (loop) in it near the bottom and tie a figure eight into that bight to clip into the biner(s) of the bottom anchor. You should place the bight so that you need to pull strongly on the rope in order to clip into the anchor, so that when the rope is in place it is quite taut and has no slack along the ground.
That's almost it. Get into your climbing harness, and run a locking carabiner through the top and bottom harness bands (not the belay loop). Position yourself at the top anchor, open the pulley and place it over the rope, and clip your 'biner onto the pulley *and lock it*. Now take a deep breath and leap into the void.
Screaming is recommended.
This is dangerous. I fell right out of the tree the first time I set one of these up because in my excitement I forgot to connect the rope to the top anchor. Friction from the rope wrapping once around the branch is all that saved me from being two or three inches shorter. Check the harness, anchors, and pulley after each ride; do not assume that because the first person did not fall to his death that it's safe from here on out.
Your rope should be of the kernmantle type and have no kinks, flat spots or heat/chemical damage. Braided or twisted rope will heat up whatever is sliding on it a lot, and could rudely interrupt your ride by parting. The rope should be neither static (no stretch) nor a bungee (30-50% stretch). Suitable climbing ropes have about 6% stretch. If you are setting up a permanent zip line you should use stainless steel cable, which requires mechanical tensioners and is beyond the scope of this node.
Note that it is possible to simply tie the rope itself to your top and bottom anchor points, and dispense with webbing anchors entirely. If you do this, be sure to wrap the rope several turns around the anchor point so that friction rather than the knot does the work of holding, and obviously you should choose an anchor point without sharp edges. However, webbing is used for a very good reason: anchors endure a lot of rubbing, scraping and stress as they are shock-loaded. This can cause significant wear, and webbing is much cheaper to replace than climbing rope, and it shows wear more obviously. The webbing/carabiner method does involve more chances for a weak link in the chain, however, so there's a trade-off between the transparency of simplicity and the strength of redundant backups.
Some people also dispense with the harness too and simply hold onto a loop of webbing attached to a 'biner or pulley. These tend to be the same people who climb solo, and they seem to be steadily removing themselves from the gene pool. Doing it this way can give you a wild ride if your center of gravity starts off to one side of the rope, and is best left to zip lines over water, which can be a lot of fun.
Use the knots as described. Granny knots are not the only type that can fail in use, and the knots above were chosen because they have the requisite strength and distribute stress to the rope or webbing in a way that does not unduly weaken them. If you don't know what a water knot is and why it's the preferred knot for nylon tape webbing, follow the link and learn it. Likewise, don't just turn a half hitch into your rope and clip that into the anchor; half hitches create a weak point in the rope under stress, while figure eights minimize that weakness.
The first few times I did this we didn't use a pulley at all; we just clipped a carabiner onto the rope and slid. Then we would marvel how hot the 'biner got. This is not good, because heat can damage a climbing rope severely, and even if you unclip *instantly* at the end of your ride, that smoking-hot carabiner tends to melt flat spots into your rope. Use a pulley. And don't use a plastic gear-hauling pulley; use a metal people-ferrying one. The unpleasant fact is that no matter how you do it, zipping wears a rope out just as rappelling does. If you do an afternoon's worth of zipping on a rope, you should retire it from climbing use and keep it for its new purpose.