Google Analytics has quickly become the website traffic analysis application of choice for small and medium sized businesses, because it does just about everything you could want, and it's priced really attractively (that'll be free then).
But although it's fairly easy to set up, there's a steep learning curve if you're really going to get anything useful out of it. Books have been written, and training courses are available, but one of the best resources I've seen has been produced by the Marketing Optimization Blog. Sure, it's just a list of links, but all you see there is the tip of the iceberg: behind those links lie weeks' worth of study. If you've got that much time to spare, that is.
Check out The Missing Google Analytics Manual and you'll see what I mean.