Probably the best way to start is the way most of us started: get the books and make some characters on your own. Of course, as Oniya and RubySlippers pointed out, you no longer need to buy the books in all cases - sometimes rulesets are available for free.
DND 3rd edition was OGL (open game licence), which means that the rules were not copyrighted and anyone could use them for free. If you ever hear of d20 rulesets, they're probably based on DND 3.0 rules, which used a 20-sided die for most rolls. DND 4th edition was no longer OGL.
Paizo publishes the game, Pathfinder, which is a d20 game based on the DND 3.0 rules. They had published DND's magazines, Dungeon and Dragon, before DND brought the magazines in-house and online, so they had a lot of credibility with players who wanted to keep playing the OGL rules.
All their rules are available online in the Pathfinder Reference Document (PRD). You can also navigate to them through Paizo's homepage. Look for "Rules Archive (PRD)" under "Pathfinder Roleplaying Game" in the left-hand navigation menu. Start with the "Core Rulebook".
I hope it helps!