I am a beginner at this great game, and I would like to improve my skills at the game of Go. What resources would you recommend?
Once you have learned some basic strategy, the best way to learn is to play. If you don't have a friend or neighbor to play with, then I highly recommend the American Go Association. They have a great resources page, links to clubs, books and teaching software.
The AGA maintains a list of Internet Go Servers for on-line play, including some turn-based servers. Turn-based servers are good for beginners because there is no pressure to move quickly — you play via email. The Dragon Go Server is dedicated to Go.
The great thing about Go is that it is easy to handicap. You and a much more accomplished player can both enjoy a game together, you just have to handicap the expert player.
The interactive way to Go. It is only rudiments, but helpful at the beginning.
Only one advice: Play on small boards !
Just start by understanding a "simplified-but-faithful" formulation of the rules, like Strasbourg Rules, and then practice with a partner (either a beginner or an experienced player) on a 5x5 board.
Once you both feel too cramped on 5x5 (typically after 5 to 10 games) then move to 7x7, and so on.
Only after quite a long time does it become enjoyable to play on 19x19. Don't try it too soon, or you'll be disoriented by the many possibilities and loose interest in the game.
Mac Software. It hasn't been updated in a while, and I have no idea if they're interested in porting it to iOS, but a company in Switzerland called Sente have produced a very nice, and free, Go client for OSX called Goban (and it still works on Snow Leopard, despite not having updates since 2006). It lets you play against the Gnu-Go program (which it bundles), and it lets you connect to internet Go servers that support Go Modem and Go Text protocols. How good you think the opposing play AI is, well, I'm not sure an experienced Go player would appreciate it, but I sure do as a learner.
At one point, I was able to download and compile up a simple Go Server for OSX on my own, so I could host my own Go Server and then people at my workplace could connect to it and we could play games over our intranet, but I wouldn't recommend that for the non-technical.
Books. Kiseido publishes a series of books on Go, in English. I have K31 ("The Second Book of Go"), which I thought was quite useful, and most of the Elementary Go Series (K10-K15), and, again, I found them quite useful. K31 says that it assumes that "you're new to the game, but you've already read a newbie intro book on Go", but I didn't think it was necessary. Once you know the rules, I thought that K31 was a perfectly fine place to start your studies.
I don't consider myself anything more than a beginner, and I also am not the sort of person who enjoys reading series of problems and such, so I haven't progressed past these books from Kiseido, but they do offer a whole raft of books for players of all skill levels (ostensibly).
Start by playing with "strong" (or at least stronger) players if you can. You'll get whipped, but at least you'll learn some of their "typical" moves.
After you have served an "apprenticeship," then look for opponents close to your own strength. Try to beat them with the techniques you have learned from others.