I woudol like to put a sink in my basement on a 35" high cabinet that sits right in front of the soil stack around which I have built a wall. Can I just tap into the soil stack for the drainage and what would be the necessary height and setup of the plumbing.

You may or may not be able to simply tap in. probably yes, but a vent is required.

I woudol like to put a sink in my basement on a 35" high cabinet that sits right in front of the soil stack around which I have built a wall. Can I just tap into the soil stack for the drainage and what would be the necessary height and setup of the plumbing.
If it's a lavatory sink, then 19 to 22" is a good height for the drain center from the finished floor.

If it's a laundry or kitchen sink, then figure between 14 to 16" to the center of the drain.

And Doug's right, you will need to vent the new drain, otherwise the trap will suction dry when the soil stack is in use.