How to wire two light bulb sockets inside a ceiling fixture?
If you pulled the wire from the socket then the best way to repair this is to replace the socket unless it happens to have screw terminals on it (I doubt it).  If you mistakenly removed a wire nut then you can easily correct this.  Wire all black wires together, all whites together, and the grounds together with wire nuts (often they are supplied with the fixture).

The lights should be wired in parallel (white-to-white, etc.), not series.  Do not wire black-to-white and black-to-white.

If you are unsure of how to make this repair then the safest thing to do is replace the fixture and/or consult an electrician.