It is hard to tell from your photo if it just callused or if there is some rot.

When cutting, you should make sure you cut all rot off. Best is to keep cutting off slices until the flesh is of uniform color - no black spots/lines remaining. Then it needs to callus - for how long depends on thickness of the plant; how much moisture is in it; temps where the plant is. It may help to dust lightly with a fungicide (sulfur; or ground cinnamon), may not be needed. Usually, few days is enough. Pot up in well draining mix. I would not water until there are roots forming - usually new growth starts by then. But at least 1week. That worked for me in the past. After, start watering as any other succulent.

I think I just picked up a few of the same thing. San Pedro? Mine looked pretty dried out at the base. The guy was so stoned (maybe on the plant? That he was unclear on potting up! )

Look up San pedro. Not legal in some countries due to hallucinogenic properties, but rarely busted unless packaging for sale. I won't be munching on it, just enjoying the huge flowers!

Looks like you've got a pachycereus marginatus there. The rot may have stopped, but it may be worth cutting again, with a sharp, sterilised blade, approx 2-3" above the current cut. I'd then lay it on it's side for about a day in an area that receives gentle but consistent airflow to encourage the callous to form. Then stand it back up, on top of a dry, very gritty mix and give it as much bright indirect light as you can. Bonus points if you can increase the rH to between 50-75% (this will aid in rooting generally speaking but it's not necessary). The humidity portion is also only helpful if you can maintain some airflow. Stagnant humidity will aid bacteria/fungal growth more than your cactus.

From there it's a waiting game. These cacti are generally very hardy and prolific, but yours has had a go of it already so you've got to keep in mind that it's not starting from the most optimal conditions. I've no doubt you'll be able to turn it around, but it will take some time and extra attention until it gets reestablished.

Try not to jostle it or constantly pull it up to check and see if it has roots. If after about a week and a half to two weeks it seems stable (as in it hasn't wrinkled super dramatically and the rot hasn't moved further up the cactus) you could try lightly watering or spraying the soil near the base of the cactus. This bare amount of moisture can assist some baby roots that may be poking out or encourage some if none have started yet. It can be tricky though because moisture is exactly what the fungi and bacteria associated w/ rot also love, so try to avoid getting the base of the cactus wet if you do choose to add some moisture. You can also just wait and hope the cactus throws some roots out in search of moisture. Good luck.

As it dries out, should I have it on a bed of soil?