Find a credit card with cash back rewards. Use the card each month for something that you would buy anyway. For example, use your card to pay for the gas in your vehicle. Or use your card to pay for your cell phone or internet bill. Then, when the credit card bill arrives, PAY IT IN FULL. Avoid carrying a balance.
Keep your usage low. Using 10% or less of your available credit line will help build your score quicker. It isn't about using a lot of credit. It is about using the credit you have responsibly. If you max out your card then it hurts your score.
Building a good score takes time. On average, it takes about two years to get a great score.
One other tip. The age of your oldest account helps your score. Try to be sure the first card you open is a decent one that you would want to keep for many years. Closing your oldest account can hurt the score you would have worked so hard to build.
BTW, people get into trouble with their credit when they use their cards to buy things that they should have waited until they could pay cash for. For example, you don't really need a $2,000 computer until you can afford to pay cash for that $2,000 computer. Buying on credit is best used for the kinds of purchases that are almost impossible to save up for, such as a car or a home mortgage. Credit cards are best saved for unexpected emergencies, such as auto repairs or home repairs that happen unexpectedly. Using only small amounts on the card to build credit is the best way to get started.