I had an issue like that on my wife's Nissan. Turned out to be the system was overcharged and once it got to operating pressure after a few minutes of the AC being on, the compressor would shut off to avoid damage. Get a AC system pressure gauge at an auto parts store. They're similar to tire pressure gauges but have an attachment on the end for the low pressure side on your AC lines. Your pressure should be around 20-40 psi for the low pressure side. Check a hayes or helms to get the exact pressure. Anyway, if it's too high, let a little refrigerant out until the system is at the correct pressure.

That might not be the problem, but if it is, it's a pretty easy fix. You could just take it in too. An honest mechanic will just tell you it's overcharged and maybe charge you a couple bucks. But a dishonest one will tell you you're entire AC system is fried and it's going to cost you $4000 to replace (lol). Good luck.