How do you find the average seek time on a computer hard drive?

Typically, this is on the manufacturing specifications of the harddrive and can be found online looking up the model. However, this particular figure is highly misleading and represents either 'best theoretical performance' or in some cases is only representative of the best performance of such speed of drives and not that particular drive. For example, nearly every SATA 2 harddrive at 7200 RPM advertises 8.9ms seek time, when in fact most cannot top 9.5ms. Some may be as poor as 14ms.
Based on these averages, most HDDs as of SATA can (and by manufacturers are) represented as such:
5400 RPM: 9.8ms
7200 RPM: 8.9ms
10,000 RPM: 4.5ms
15,000 RPM: 3.3ms

However for a real, accurate read, I suggest using a program such as HDTach, SiSoft Sandra, or even the Windows Vista system specifications benchmark (although it doesn't give much detail, it can give you an idea of how it stacks up against others)

Note also that the seek time of a harddrive varies based on task.

For example:
Reading from the outer edges of the disk much faster due to the laws of centripetal force. The outer edge spins faster than the inner edge.
Sequantial reads (one file, non-fragmented, or multiple non-fragmented files directly beside each other read in a series) are faster than random reads and fragmented files.

A single fragment effectively doubles or worse the load time of a single file. So a file split into many pieces takes considerably longer to load.

Keep in mind that even the world's fastest hard drives (15,000 RPM SCSIs) are only an average of 140 MB/s or less, while your RAM is typically going to be 6,400 MB/s or better (for DDR2 800 MHz)
This should give you an idea of the enormous gap between the harddrive and the rest of the system's capabilities.

Solid State Drives are a drastic improvement. Their seek time is measures in microseconds rather than milliseconds. Most average around 0.45ms (or 450 microseconds) seek time for reads, but as high as 100ms for writes. This can cause 'stuttering', because Hard Drives are usually only 1/2 as fast for writes as reads. SSDs can vary wildly in their read time as well, from under 20 MB/s to over 300 MB/s. They tend to be much smaller and more expensive per GB than HDDs, so many people still have not adopted them. They also have the advantage of being much smaller and lighter, using less power, and having no moving parts they theoretically last much, much longer. However, the components in an SSD wear out each time you write to it, so using a SSD for constant writes (such as swapfiles, temp folders, and caches) can cause it to last equal or less time than a Hard Drive. SSDs are not typically damaged by shock, movement, or being dropped like HDDs, and most can withstand 50Gs of force or more onto a hard surface. They must be physically broken or snapped, typically, to break them.