If the smoke coming from your lawn mower is black and it won't run, that is usually a case where the ratio of air to gasoline is too much, as in the mower is taking in too much gas. For situations like this, check the choke. The mower needs lots of gas to start, but the choke is supposed to cut back on the supply once running. However, it sometimes sticks and won't move into place, so make sure it's clean.
Colored smoke can also mean a clogged air filter. This filters are often paper or foam. Paper filters need replacing, but foam ones can be cleaned and recharged with a little engine oil.
Burning oil and carbureator problems can also mean lawn mower smoke, but diagnosis and repair probably require professional servicing.
If the engine does run and the smoke is blue or white, then it's usually easier cases like the wrong oil grade, too much oil, the engine being tilted more than 15 degrees or worn parts.
If yours seems to be running and sounding okay but is just producing smoke, it might be just burning out crud hardened over the winter. I'd just look it over to see if everything looks right and check the fluid levels. Try it out for 10 minutes and see if the smoke continues; it may just clean itself out.