How to cover an open/exposed wire fast and safe for a long period?
What you want to do is terminate the wires in the junction box using Wire Nuts.  Simply thread them on to the end of the exposed wire, and you need not worry about live wires touching, kids getting zapped, etc.  You should turn off the branch circuit in question (via a circuit breaker or removing a fuse) while removing the outlet and putting on the wire nuts.

If you need to have the box open for a more extended period of time, get a flat cover plate for the junction box (put on the wire nuts, tuck the wire back in the box, attach the cover plate).