You can get a smoky mower from a worn out engine, or it can be something a lot simpler.  If the mower was tipped on its side, or the air filter was badly plugged it may have pulled oil from the crankcase into the cylinder and then into the muffler.  This one had a plugged air filter and sucked the oil through the breather, through the engine (fouling the spark plug), and then filling up the muffler and spewing onto the deck.  You can't see it in this photo, but there's a big white cloud coming out of the exhaust.  See the little ghost of a black spot on the deck by the muffler?  That's a hint that it's also running rich.

Once you've fixed the problem of oil in the exhaust, there is always enough in the muffler to smoke for what seems like forever!  What I do is remove the muffler is remove it and spray a little carb cleaner into it, then drop it into a coffee can of hot water and liquid dish detergent.  That will cut the oil out and should start it running clean again.

See the old slobber mark (now facing sideways) on the muffler?  That was the oil pumping out of the muffler before I fixed it.  Now wipe up that oil mess on the deck!