From Cancun

There are frequent buses from the central bus station in downtown Cancun, and the fare should be only around 20 pesos ($2-$3).  Some of the buses are fairly luxurious long distance services on the way to Chetumal (and are more expensive), others are more basic but comfortable.

From Airport

You'll have to take one of the exorbitantly expensive taxis to downtown Cancun - pay at the booth in the airport building.  There isn't any choice as taxis are not allowed to pick up customers here except through this arrangement.  For a private taxi you'll pay around 240 pesos ($30) for the short distance, share a cab and it is quite a bit cheaper.  You could also check the fares for a direct taxi to Playa del Carmen at the same stand.