When you have too many credit cards, closing some of them is a good way to simplify your financial life. Before you make that phone call, first make sure closing these credit cards won't hurt your credit score (See Five Credit Cards You Should Never Close).
Once you're sure closing the credit card is the right move to make, follow these steps to make sure the card is closed in your favor.
Contact Customer Service
Call the customer service number on the back of your credit card. Let the customer service representative know you'd like to close your credit card account. Don't be surprised if the representative tries to talk you into keeping your account open. If you're sure you want to close the account, don't allow yourself to be convinced otherwise. Note the date and time you made this request.
Follow-Up With a Letter
Follow up in writing to have a record that you requested your credit card to be closed. In the letter include your name, address, and credit credit card number (or at least the last four digits of the card number). State that you made a request by phone to have your account closed on such-and-such date and you want your credit record to reflect the account was closed at your request.
Update Your Records
Keep a copy of the letter for yourself. Send it certified mail so you have proof the letter was mail and received should that fact ever come into question.