Ok, antimagic is the simpler of the two so I'll start there. I don't really know what the book says about it, but in every game I've ever run or been in, Prime 2 allows you to basically project antimagic which works to negate incoming effects or unweave standing effects. This is not intuitive, it must be focussed.

Countermagic is more complicated and more fun. If you know someone is going to hit you with and effect and you have the same spheres you think they're going to throw at you then you can declare that when he does that, you do it back. This results in whoever loses the contests roll gets hit by the effect. You can also do other strange sphere v sphere effects like, "I know he likes to annimate matter and have it bite people so when I see him do that, I'm going to instantly blow that matter to hell with Forces 3."