Those gas canisters are really simple. You just screw them in and out of their housing.
A visual inspection will tell you whether the lid has been broken (assuming the inflated vest doesn't give you a clue), and if you want to be 100% sure that the CO2 is still in there, all you need is some accurate kitchen scales.
As for the jacket itself, blow it up manually using the inflation tube (with a low-pressure air pump preferably to prevent introduction of a lot of moisture, like when you would when inflating it orally), then let it sit for 24 hours (maybe with a bit of weight on it) to see if it doesn't leak.