As someone who just recently started playing Civilization 4 myself (about 2 months ago), I'd suggest buying Civ IV Complete and starting with Beyond the Sword.
I had only been playing Civ IV for about 3-4 weeks when I got BtS and I found the transition quite difficult. I had played a lot of Civ IV in those 3-4 weeks and went from Chieften (winning my first game), to Noble (losing my first 4-5 games), to Pince (again losing 4-5 games), but when I got BtS I had to go back down in difficulty to Noble and I still lost my first couple games.
If you have never played any Civilization game before, then I would suggest:
first) reading the manual
second) playing a game at the easiest difficulty (Settler)
third) moving up in difficulty levels one at a time until you lose a game, at which point you should visit the war academy here and read some of the articles.
Don't be discouraged if you aren't good at the game right way. I have a friend who has been playing Civ IV off and on for about a year and he still hasn't won a game at Prince. However, he doesn't come to this forum or read the articles on the main site. Honestly, the only way I got past Noble was by reading the articles on this site and reading advice threads in the forum. Don't be afraid to ask for help either; (most) people on the forum will be more than happy to give you advice. Just ignore the infantile bickering that some of the posters ingage in and have fun.