Before making an electrical connection, you must strip the insulation from the end of a wire. This is a simple process, but it's important to do it right so you don't damage the copper wire. Use a stripper instead of a knife or wire cutter.
It takes a little practice to learn how to make firm splices. The right tool is essential: Nothing does the job like a pair of lineman's pliers. Always take a few moments to check your work. Check the bare wire after you strip it to make sure it is not gouged. After splicing wires and adding the correct size wire nut, tug on the wires to make sure they are securely joined.
The insulation should slide off easily, with no more than a slight mark on the wire. If you have to pull hard or the stripper leaves a nick or scrapes the wire, check that you are using the right hole in the stripper. If the problem persists, buy a new stripper.