Check the cables to the battery first. I replaced a battery and an alternator a few days ago, and had this same problem after. All it was was the cables that connect to the battery needed a tightening. They could probably use a clean as well. There is a little brush like thing you can get for like $5. Like a pipecleaner.
To check the alternator, take a broom handle, has to be completely wooden, or something like a broom handle, have the car running, stick the handle on the alternator and put your ear to the handle. If you can hear any knocking or grinding, it's going.
Also, when you come to a stop, is there a high pitched whine? Even a really quiet one? That was the clear sign that mine was going to go, and 10 minutes later I shut the car off and couldn't start it again.