If your Home Depot is like the ones around here, you can buy a handful of pulleys and a hundred feet of rope for about $30. The pulleys come in a variety of kinds, but the kind I like best for mechanics toys are the large plastic “clothesline pulleys”, like this:
A Zip Line
One of the simplest things you can do with pulleys is to make a “zip line.” If you have a long rope or cable, with one end higher than another, and drawn taut enough so that it doesn’t sag in the middle, you can hang something on a pulley on the rope, and it will roll down the rope from the high end to the low end. Sometimes people ride down such a line for recreation. NASA used such a system to allow astronauts to quickly escape and get far away from the space shuttle on the launch pad, should such an escape ever become necessary. You can make a toy zip line at home in a couple of minutes.
You just tie a pulley to a teddy bear or something, then get a really long rope and tie it to something at both ends. Make sure it is drawn taut enough so that it doesn’t sag in the middle, with one end higher than the other. Make the upper end easy to untie and re-tie. Then you just untie it, put the pulley on the rope, and let it run down.
A much more complicated contraption would be a block-and-tackle system for lifting heavy weights. I made mine by fastening together two sets of three pulleys. I used strips of “punched sheet metal,” cut to length with my bolt-cutters, and with the three pulleys bolted through the holes, but you could also use strips of wood with holes drilled into them. You need two blocks, or two sets of pulleys: an upper block to attach to the upper mounting, and a lower block to attach to the weight you wish to lift. You also need a way to fasten the two blocks to their respective mountings. You could just tie them to their mounts with a short fastening rope through holes in the flat strips, but as long as you are bolting together three pulleys, why not include a couple of hooks or loops as well? Then you can easily run the fastening rope through the loops. I used a pair of “anchor shackles” in one of my blocks, and a pair of “spring links” in the other, and they both worked reasonably well. All of the equipment I bought was in the same store as the pulleys, a few paces away.
After assembling and mounting your two blocks–the upper block to a tree branch or swing set or something, and the lower one to something heavy, like a $1 concrete block from the same hardware store–you rig the rope. Assuming you have two blocks of three pulleys each, start by tying one end of the rope to the frame or tree branch or to one of the anchor shackles of the upper block. Then you run the rope down and under the first lower pulley, up and over the first upper pulley, down and under the second lower pulley, and so forth, until the rope comes out and over the last upper pulley. Plan on spending a long time rigging the pulleys–it can be quite an annoying chore.
When you are all done, and the rope runs freely through all of the pulleys, you should be able to pull down on the free end of the rope, and slowly but easily lift the heavy weight.