Here's how you should be able to get your first one without any hassles.
In the mid of the credit crunch, it became harder to get a credit card as easily as it was 3 years ago for instance. The cards that were easy to apply to and get instantly are harder than before. But, there's always a way to get your hands on one that will not make your life hard.
Most people get credit cards when they're in college, although, not the best time to get one, it has proven to be easier than getting other kinds of cards.
When in college, you will be getting a lot of offers from your bank and other credit companies saying that you are eligible for student cards. Do your research and check which one will suit you best. I say go with the one with the lowest credit line, they usually do not charge you a lot (interest rate wise that is).
If you are not a student, there are still easy ways to get your first credit card, do not just get the one that your banker recommended, go online and offline and do your due diligence and research on all the ones you think are good for you and you will see how glad you will be by doing that research. Some banks and companies lie, most others hide some unpleasant facts about their offer, do your best in finding out about them before you apply to anything.