To make the basic stand, you need a five-gallon bucket, 20 inches of 2-1/2-inch diameter PVC pipe, and some concrete--as well as a trowel and tools needed to mix and manipulate concrete. An assistant is probably a very good idea. Make up a thick mixture of concrete. Place the bucket in the position you'll want to keep it, because when you fill it up, the bucket will weigh 50 to 60 pounds. Center the tube in the bucket, sticking completely upright, then pour the concrete mixture in. Use a trowel or a piece of wood to tamp the mixture down. Leave the stand to dry overnight and place the umbrella in.
If the stand is going in place under a table, you could cut the bucket in half first. This will allow the stand to fit in place and the table itself will make up the difference in height.
The bucket handle will break after the concrete is loaded into the bucket. You could build a simple handle out of metal or rebar--insert these handles through the plastic bucket before the concrete goes in. If you have a full sized-bucket, you can press some decorative shells, rocks or marbles into the concrete before it dries. Decorate the sides with some acrylic paints. This will make the bucket a little more attractive, especially if you have several umbrella stands in your yard.
The most decorative option is to use a large decorative plant pot instead of a five-gallon bucket. Ideally, get a plant pot that's about as tall as a bucket. Use the same length of pipe, but about half of the concrete. Center the pipe, pour in the concrete and tamp it down as above. The difference this time is after drying, pour some potting soil in over the concrete and plant some flowers around the standing tube.