It can take as little as 6 months, but... in all honesty, the first few months you have a new account open, your score is automatically based on a more sympathetic calculation, so... no matter where you're at in your credit, your score will look a few points better in the first few months of having a new account open.
One thing you should check before getting a credit card, though - make sure they DO report to the bureaus. Some gas credit cards and department store cards don't, so... if they don't report, you don't get a great score.
You might want to think about getting a secured loan first - I do that every year with my tax return. It doesn't affect what kind of cash flow I have, I give my bank $1,000, they stick it in my savings account (I can't touch it there), and they give me $1,000. Every month on the due date, they take the payment amount out of my savings account, and I don't have to do a single thing. As long as your payments are for 6 months or longer, it builds credit.