There are a few places to play it online. If you would like to play it in real time, I recommend the following websites:
http://www.playok.com
PlayOK is a website offered in a variety of languages and is the most popular real-time shogi playing site on the internet. You'll meet people from all over the world on this site, many of whom speak English. It's also full of beginners and lower-ranked players, so after a bit of playing you should be able to get some wins if you stay within your strength bracket.
http://www.shogidojo.com
Shogi Club 24 is a Japanese website and, as far as I know, the biggest shogi playing site on the internet. Every time I log onto it there are more than 3,000 players of varying levels playing at the same time. There is an option for an English site so you won't be lost trying to navigate it. SC24 is, however, full of very strong players.
I'm not too experienced with these sites, but if you prefer correspondence shogi (where each player has several days to make a move), then I recommend the following sites:
http://www.brainking.com
Brain King offers many games, and it has what I believe to be one of the biggest western shogi communities on the internet.
http://www.goldtoken.com
Gold Token is pretty new, and also offers shogi.