Some people will tell you that you should allocate twice as much swap space as you have physical memory, but this is a bogus rule. Here's how to do it properly:
Estimate your total memory needs. This is the largest amount of memory you'll probably need at a time, that is the sum of the memory requirements of all the programs you want to run at the same time. This can be done by running at the same time all the programs you are likely to ever be running at the same time.
For instance, if you want to run X, you should allocate about 8 MB for it, gcc wants several megabytes (some files need an unusually large amount, up to tens of megabytes, but usually about four should do), and so on. The kernel will use about a megabyte by itself, and the usual shells and other small utilities perhaps a few hundred kilobytes (say a megabyte together). There is no need to try to be exact, rough estimates are fine, but you might want to be on the pessimistic side.
Remember that if there are going to be several people using the system at the same time, they are all going to consume memory. However, if two people run the same program at the same time, the total memory consumption is usually not double, since code pages and shared libraries exist only once.
The free and ps commands are useful for estimating the memory needs.
Add some security to the estimate in step 1. This is because estimates of program sizes will probably be wrong, because you'll probably forget some programs you want to run, and to make certain that you have some extra space just in case. A couple of megabytes should be fine. (It is better to allocate too much than too little swap space, but there's no need to over-do it and allocate the whole disk, since unused swap space is wasted space; see later about adding more swap.) Also, since it is nicer to deal with even numbers, you can round the value up to the next full megabyte.
Based on the computations above, you know how much memory you'll be needing in total. So, in order to allocate swap space, you just need to subtract the size of your physical memory from the total memory needed, and you know how much swap space you need. (On some versions of UNIX, you need to allocate space for an image of the physical memory as well, so the amount computed in step 2 is what you need and you shouldn't do the subtraction.)
If your calculated swap space is very much larger than your physical memory (more than a couple times larger), you should probably invest in more physical memory, otherwise performance will be too low.
It's a good idea to have at least some swap space, even if your calculations indicate that you need none. Linux uses swap space somewhat aggressively, so that as much physical memory as possible can be kept free. Linux will swap out memory pages that have not been used, even if the memory is not yet needed for anything. This avoids waiting for swapping when it is needed: the swapping can be done earlier, when the disk is otherwise idle.
Swap space can be divided among several disks. This can sometimes improve performance, depending on the relative speeds of the disks and the access patterns of the disks. You might want to experiment with a few schemes, but be aware that doing the experiments properly is quite difficult. You should not believe claims that any one scheme is superior to any other, since it won't always be true.