My Fingers Hurt

A little bit of discomfort can be expected at first, because your fingertips are pressing on metal wires.  After a while, though, they develop protective callouses, and you will not even notice any discomfort.

If your fingers hurt because you've been slamming them against the fingerboard (which is possible, especially if you hear a "thump, thump" sound with every note you produce) you might want to have the action on your mandolin raised.  "Action" refers to the distance between the strings and the fingerboard.  Ideally, the action should be set so that the strings have some resistance, but not enough resistance so that you can't press the strings down without difficulty.  The amount of resistance required is different for each player, so the only thing to do here is to experiment.

If your fingers hurt because you've been stretching them while practicing chords, the only thing you can do is try some exercises that specifically stretch the muscles in your fingers.  There are some good exercises in the Exercise section of this site, and the best part is that you can do these exercises anywhere, any time.  Even with exercises and practice, some people still find it difficult to stretch their fingers far enough to play chords especially if they have small hands.  Playing your mandolin should not be a painful experience.  If you're finding this painful, then consider playing three-finger or two-finger chords at first.