I just applied and was approved a credit card, I am about to apply another one, how long should I wait?
The formulas for calculating credit scores are designed to judge certain credit behaviors as negative or positive, and in different degrees. One of these behaviors is applying for credit, which results in a "hard inquiry" of your credit file.
Typically, multiple hard inquiries in a very short time span reflects that you are shopping for the best credit deal — a positive behavior. This aspect of the credit scoring formula was designed to avoid negative effects for consumers who shopped around when looking for the best auto loans or mortgages.
On the other hand, hard inquiries into your credit file that appear sporadic may reflect poorly. From my research, all your credit shopping should occur within a two weeks. This would require planning (which is why credit scoring models usually do not penalize for multiple hard inquiries in such a short time span). If it's been longer than two weeks, it may appear sporadic to the credit scoring formula, which is not good.
Hard inquiries are not the only factor in your credit score. The fact that you are adding available credit can have an impact (either positive or negative depending on other factors… it gets a bit complicated). If your first accomplishment with this new card is to add a huge balance to it, especially if that balance is over 50% of the credit limit, then that will not reflect well on your credit score (this is your debt-to-available-credit ratio and is part of the "Amounts Owed" factor that accounts for 30% of your score).
Evaluate why you are applying for more than one credit card. If it is for the "purchasing power" then you should re-evaluate. The illusion of purchasing power given by owning a credit card is what gets many people in trouble. What you are really doing is borrowing against your future earnings (this is the basic concept of credit). The more you borrow, the less of a future you have.
If you are concerned about your credit score, please use the links below to learn more about credit scoring. By far, payment history is the most important factor in credit scores. So, if you get in over your head with debt and are unable to keep up, your efforts at safeguarding your credit score will be lost.
So, apply for and use credit wisely (it is best not to use credit cards at all). Always pay your bills on time. If you can (and you should), pay off the entire balance each month — carrying a balance on a credit card is expensive and a waste of money (interest will eat up your income). If you are unable to fully pay off the balance, keep your balance below 50% of the credit limit (for example, $500 balance on a $1000 credit limit). Only use credit cards for convenience, not for an actual loan — credit cards offer the most expensive loans (besides payday loans) with the worst terms that the credit card company can change at any time (with 15 days written notice).
The only legitimate reason to own a credit card is for car rentals because some car rental places will not accept anything else. The same is true for some hotels (they require a credit card for reservations and will not accept a debit card). Although a credit card may provide some payment convenience for day-to-day purcahses, this convenience will vanish when you receive your statement unless you accounted for every single purchase (plus your credit card's fees and interest) and subtracted that amount from your bank balance when budgeting.