Many people worry about being seen as "too clingy" if they call right after a first date.
A generation or two ago, there were more traditional rules to dating (think back to middle or high school dates where you had to meet each other's parents before being allowed out). The general rule was to wait at least two to three days before calling so as not to seem too eager.
A More Modern Take
However, just because you wait to ask for a second date does not mean that you have to cease all contact.
Often by the end of a first date two people will verbally establish their desire (or not) to see the other person again.
Whether or not you have made plans to see each other for a second time, a follow-up phone call is a thoughtful way to show your date that you appreciate his time and company.
You don't have to speak for hours on the phone or stay up chatting on the Internet; a few simple words are enough to flatter your date and help your chances for seeing her again.