Here's my list of 5 things to do:
First thing's first take it apart down to the bare frame and make sure everything has adequate grease. That will make a HUGE difference in how it rides.
Second shed any weight you can, If it has steel cranks like my Mongoose Beast had swap them for aluminum.
Third check tire pressure, improperly inflated tires can cause the bike to feel sluggish if they are low or if they are over inflated the ride quality can be bumpy.
Fourth make sure everything is adjusted properly (Cone nuts on wheels, cranks, chain tension, exc.) Having an overtightened crank or cone nut on a wheel can cause premature wear and also drag on the bike causing it to feel sluggish.
Fifth upgrade components, this is where you can get expensive, derailleurs, shifters, grips, seats, tires, rims, exc. Upgrade to lighter / stronger / better components.