Though a lawnmower blade doesn't have to be significantly sharp to effectively turn leaves into mulch, as much sharpness as possible is ideal. If you're running the lawnmower over the leaves with little mulching taking place, turn off the mower and turn it on its side. Use a wrench to remove the mower's blade, and then sharpen the blade's cutting edges on a grinding wheel. Mount the blade back on the mower and try again.
If you use a ride-on lawnmower to cut your grass and mulch your leaves, it will likely have two or more cutting blades. Unlike a standard push mower, ride-on mower blades are driven by a belt attached the motor. If your ride-on tractor isn't showing signs of mulching the leaves, the belt may be off. Turn off the mower, raise the mower deck and check the belt. If it's loosened to the point of coming off, put it back on its pulley and tighten it with the adjacent lever.
A benefit to having a lawnmower with an adjustable deck is that you can set it precisely to cut your grass. For mulching, you might also have to adjust the deck to ensure the spinning blade isn't passing over the leaves. Most decks are adjustable by a lever or a set of cotter pins; try lowering the deck and see if you're able to have better results.
Trying to mulch the leaves in your yard when they're wet and soggy doesn't work well. If the leaves are wet, they'll clog the lawnmower's output and build up around the blade. After a period of use, the lawnmower may not yield the results you wish to achieve. Turn the mower off, turn it on its side and clean out the soggy leaves. Ideally, wait for a dry day to complete the mulching job.