When stripping wire using the tools in the lab, you will need to hold the wire quite firmly and identify the correct thickness of hole.
It is easy to find the correct thickness for your wire by starting with a larger hole and working your way down. A little bit of trail and error will soon result in the correct hole being found.
You will need to strip approximately 10mm of the plastic sleeving to effectively fit single core wire into a Breadboard.
If you are stripping the wires for other purposes then use your discretion to select the correct length.