If it's a SRAM chain then it'll have a gold link somewhere along the chain. This is the power link, squeeze the link together and push the chain together at that spot and the link should break free, it slides along a small rail and pops into place when it's locked in. so all you have to do is pop it out.
if it's a SHIMANO chain you need a chain tool and a new chain pin. You want to pop a pin off of a leader portion of the link, so take the chain above the chainstay and pop out a pin on a the front part of the round link. DO NOT try to re-use this pin as atempting to pop it back in could destroy one of the chain plates. Use the new chain pin (it should be pretty long), pop it in using the chain tool and break off the excess end that sticks out.
I'd explain this a bit clearer with a bike in front of me, sorry if I'm vague.