Fishing is a very popular pastime both within the Park boundaries of Yellowstone and outside the Park with Cooke City having an especially large number of fly-fishing outfitters. If you wish to fish within the Park you will need a permit and will need to be aware of the various regulations pertaining to fishing. The Park Service website has all the information you will need
http://www.nps.gov/yell/planyourvisit/fishing.htm
If you do not have your own equipment with you, it may well be easier to arrange an expedition with an outfitter. For a list of companies licensed to lead fishing trips within the Park go to