Chess can cost you practically nothing, which makes it the perfect homeschool elective. I've found several boards for sale in secondhand stores and garage sales. But I did break down and purchase a standard tournament board after we got into the game for a bit and began playing in tournaments.
A simple library book or three can help you learn which pieces move and how. Ages ago, we bought some sort of chess disk to play on the computer. Software isn't very expensive. For that matter, you can play for free online at http://www.chesskid.com/ or http://www.chess.com/. We bought "premium" memberships in chesskid after we tried it out for a while and figured that it was something we would really use. There are videos and tactics exercises galore.
One book I found pops up for sale frequently with homeschool curriculum providers is Starting Chess. My nine-year-old, Emperor, took a look at it lately and declared it far too simple. Which to me means that it likely is a truly "starting chess" sort of a book that most anyone would find understandable. Currently we are working through the Simon and Schuster Pocket Book of Chess. I'd recommend it for a middle school through adult beginner. It contains some basic tactic puzzles and teaches algabraic notation (the current standard) after a brief introduction of the pieces and their moves.
There are a good number of youtube videos and websites devoted to chess and chess tactics as well.
We've found there is a chess club and a chess league not too far from where we live. We've been playing at the league level for about 6 months and now we are ready to try going to the club each week. I don't think we'll ever get as ambitious as our friends who are going to NATIONALS this week in Dallas (Good luck, S family!!), but I think we'll always enjoy the game.