How do you release the wires from a push-in wire connector?
If you're talking about an outlet - or a similar concept fixture - the best tool I've found is a flat head jeweler/precision screw driver.

The wire is being held in by this:



You can see you'll need to push that "tab" away from the wire, from the back of the outlet you should see a small rectangle hole next to each circular hole that the wires are in:



MAKE SURE POWER/BREAKER IS OFF YOU WILL BE TOUCHING A "LIVE" WIRE
Insert a small jeweler screwdriver in the rectangular hole/slot, use the box as your pivot point and the screwdriver as your level (bring back end of screwdriver towards wire to force "tab" away) and gently pull the wire out. 

* If the outlet is old/weak or the wire wasn't inserted in deep you can sometimes get away with just twisting the wire back and forth while pulling.