Learn the mandolin fretboard. This eight-stringed instrument does not have the same note ratios as a guitar, so it's important to get your head around the specific tuning of the folk instrument. Different kinds of lessons are online, including the AFT method of remembering note placements on the mandolin.
Tune your strings. The specific double-string setup of the mandolin means you'll want to tune every "pair" (light and heavy string found together on the instrument) to an octave. Practice getting the tones just right by tuning each string individually with a tuning fork or electric tuner.
Find a picking style. The double-string setup also requires a strong picking style and the right kind of pick to really make the double octave notes resonate while you're playing out a mandolin melody line. Experiment with different picking techniques to see what sounds right.
Practice strumming chords without deadening strings. When you have figured out the chord structures for the mandolin (by learning the fretboard), practice fingering styles. Like other smaller string instruments, playing chords on the mandolin requires precision and careful attention to where your fingers fall when forming chords. If your fingers brush an open string, the sound can not be heard when you strum. For people with thicker fingers, this is an especially difficult part of learning. Practice holding your fingers perpendicular to the string and pressing down on a specific string set.
Follow the leader. The mandolin is hardly ever the "front" instrument in a folk band (it's usually the fiddler or singer/guitarist). Learning to play with a band means paying attention to the cues and signals held commonly by folk musicians. Get used to following along to chord progressions and song changes, from verse to chorus. This can make you much stronger on the mandolin in a group setting.