The bad news: each inquiry on your credit report lowers your FICO score. So, for all consumers, the first effect of a credit card on a FICO score is negative.
The good news: an inquiry isn't going to hurt you much. Inquiries lower your score about 2 to 3 points. Inquiries also age rapidly. After a few months, the inquiry is already beginning to fade, and after a year, it ceases to have any effect on FICO scoring at all. After two years, the inquiry drops off your credit report entirely.
N.B. Pulling your own credit report is known as a "soft pull." Soft pulls don't count against you at all, no matter how often you pull your own credit.
The bottom line: don't let inquiries stop you from applying for credit, but understand they are there, and they do add up. Ten applications for credit would likely lower your score around 25 points, and that does start to become significant. If you didn't know that when you painted the town with credit applications last month, take solace in the fact that inquiries decay fairly rapidly, so the damage you did to your credit score will heal in a few months to a year.
If you're polishing your financial brass and plan to apply for a mortgage in the next few months, you should refrain from applying for any credit cards. Inquiries show up within hours of applying for credit, immediately lowering your FICO score. Other effects will follow...some in weeks, some in months, some taking years...