To check for a bad link, slowly back pedal the bike and watch the chain as it goes through the rear derailleur....the thing that guides and changes the gears in the rear. A stuck link will not run smoothly through the derailleur. If it's just a stiff link, try taking the chain where the stiff link is and bend it back and forth a few times. Sometimes this will "release" it. Add some chain lube to the chain, too.
If you put a new chain on the bike, be aware you should change the rear gear cluster at the same time as both that cluster and chain wear as a unit. Changing the chain and not the rear cassette/freewheel will prematurely wear out the chain as it tries to match the wear pattern of the gears, and can cause the chain to begin skipping on the rear gears. If you want to take a chance, and if the chain/gears don't have a lot of miles on them (like under a 1000 miles or so), just try a new chain.
A bad bottom bracket bearing set (the bottom bracket is the thing that the crankarms/pedals attach to on the bike) can also cause noise/clicking as the bearings wear out. Isolate the bottom bracket by removing the chain from the crankset (the geared thing with the pedals) and turn the pedals and listen. Be aware sometimes bottom bracket bearings don't make noise unless under load. The bottom bracket could also be loose, or your crank arms could be loose and need retorquing....a common problem causing this type of noise you describe.
