How to calculate buoyancy?

I’ve been looking at the hundreds of formulas in this Wikipedia page but I have no idea which one is appropriate.
http://en.wikipedia.org/wiki/Buoyancy

Basically I want to calculate how much air is needed to bring a person back to the surface after it is submerged.
Let’s say a person wearing only a wetsuit dives to 10 or 15m and then inflates an air bladder with a CO2 cartridge.

I’d like to know how much air is needed or what is the force needed to bring that person back to the surface? How do I calculate that?
I’d appreciate any thoughts or calculations that can help me with this.

Anyone willing to help me out?

Thanks in advance!