Muk has got great HP, but being weak to two pivotal moves (Psychic and Earthquake) just hurts its prospects a lot. However, he does work somewhat decently in UU due to its alright stats and less Psychic Pokémon going around.
Sludge is Muk's strongest STAB attack, and so it's a given to use it. Body Slam is for the much needed paralysis, Screech is for more damage, Mega Drain is an option to use against Golem and Rhydon, and Explosion is just there to blow up on things that annoy you.
Acid Armor raises his mediocre Defense, but it's not really needed. Hyper Beam can work well with Screech. Thunderbolt and Thunder can be nice surprises for an incoming Starmie or Lapras, but don't expect it to do that much because Muk's Special is pretty low.
Checks and Counters
Muk can't touch Gengar. Psychic-types such as Alakazam, Hypno, and Exeggutor (unparalyzed) can destroy him too, though the last is not the safest switch-in due to its weakness to Sludge, especially if it's paralyzed. Rhydon and Golem of course stop him, although they need to be wary of Mega Drain, which, despite the 4x weakness, is still only a 3HKO. Muk cannot do anything to the legendary birds either, except Explode on them.
Keeping with the Ground-types trend, Nidoking, Nidoqueen, Sandslash, and Onix serve as reliable counters in the lower tiers. They all can take any of Muk's attacks (except Mega Drain in Onix's case) and serve up a STAB Earthquake.