Examining how large your cacti and pot are, will help you determine how deep you should make your hole in the potting mix. You want to make sure that your hole has enough room so that the roots of the cacti are comfortable.
I would suggest using gloves to transplant your cacti (ouch)! Take a knife and lightly dig the edges of the old soil to help ease the repotting process. Grab the base of the cacti and pull lightly from old container. Afterwards, place roots and cacti in the pre-dug hole in the potting mix.
After placing the cacti in the hole, make sure you firmly pat the soil around the base of the cacti (Not too tight, but just enough where the cacti can support itself standing straight). Add extra potting mix if necessary for support.