If you google search for it, you can find all kinds of info and even tutorials on how to do this. (They're also called Beowulf clusters; that'll help your searching.)
There are several flavors of software that can do this, so I won't get into that, but I will give a few hints about hardware;
-You'll need quite a few computers in order to make a true supercomputer; I'd say at least 100, if they're modern ones.
-You'll need some very fast network hardware (cards, cables, switches, servers) in order to keep it running smoothly; that is, unless your code is extremely well parallelized, in which case a slow network is acceptable. There have even been cases where a cluster has been run on a sneakernet (a network where a guy (wearing sneakers) carries the data on a disk from one computer to another)
-You'll need a way to power it. A normal home electrical system can't handle any but the smallest clusters.
-You'll need a way to cool it. This is easy to forget, but very important. If memory serves, the rule of thumb is one ton of air conditioning per 3 kilowatts of power being used by the cluster. Otherwise the entire room the cluster is in can overheat severely.
-You'll need somewhere to put it. The space needs not only to be big enough and well enough cooled, but it also needs to be sturdy. The weight of all those computers can add up, so if you're putting them somewhere that is above another floor, make sure that floor is sturdy enough.
