you can get a Remington 22 nail driver for concrete and just make some walls out of two by fours and drywall. your only obstacle will be how to make the walls sound and non movable since you are not going to the ceiling. This always is the issue when doing something like this. If you do not have kids that will be playing down there, then maybe this is not an issue.
I would first determine the size of the cubicle, then draw it out on the floor. See how that size sizes up for you. Most cubicles become too small when you add all the stuff, so make sure it will handle all your amenities.
Then with liquid nails and a nail gun, tack down the floor plate on both areas.
Now, at a seperate location, build your walls from 2x4 set on 16 inch centers. Decide up front about running electricity in the walls, if so drill your holes.
Now fasten the pre fab walls to the floor plate then attach to the other end of the basement walls. Us the nail driver there but with a lighter load not to crumble the cinder block if that is what you have.
Then rock it out, tape and bed and prime it and then paint it. Should be all you need.
Rem nail gun.
Level and snap string.
Lumber and rock and tape and bed stuff.