Building Your Bankroll
It's easy to learn about bankroll management but being disciplined enough to stick to it is the tough part. The first step is to put together a plan on how to build up your bankroll. You need to figure out how you'll use bonuses, winnings, etc to move up in stakes and how to know when you've moved up past your abilities.
You have to remember that if you want to be in it for the long-haul you have to plan like you would anything else worth doing. You need to figure out how much risk you're willing to accept and what you're going to do if your results at the table don't pan out.
I think a good rule of thumb for NL cash games is having at least 20 buy-ins. That isn't 20 big-bets, that's 20x the buy-in. If the buy-in is $1 you should be sitting down with about 100BB so $100. And 20 x $100 = $2,000.
For limit players there is less variance so you can get away with only sitting down with 25BB but you should still have 20 x that in your bankroll.
For Sit and Go's around 40 or 50 buy-ins will be needed to cover the variance. So if you play $10 SnG's you would want to have $400 - $500 in your bankroll to help absorb any downswings.
Multi-table tournaments are very tough because you can go long streaks without cashing. I don't really recommend multi-table tournaments for trying to build up a bankroll though. Unless you have the cash to start fairly high you'll need to start off playing lots of tournaments with huge fields which increases your variance. You would probably be better off playing SnG's or cash games and play in freerolls or wait around for low buy-in events.
But the most important part in all of this is knowing not just when to move up but when you need to move down. If you lose more than 25% of your bankroll your best bet is to move down in limits and work your way back up. There's no shame in that. It's the sign of someone with good bankroll discipline.
So make your plan, work your plan, and prosper!