Play it until it stops working. Peek in the door and see if the plunger is stuck up in the coil. If you can't see it thru the door, gently raise the field enough to get your eyes on that coil. If the plunger is stuck in the coil, turn the game off and see if it drops back down. Then replace the driver tranny.
If the plunger is at rest, lift the plunger enough to get a rag moistened with Goo-Gone in there to clean the rubber stopper. If there is no stopper order replacements. Retest. If it works, stop here. If it still doesn't work...
Go up in the head and find the chime driver tranny. Connect a jumper to the braid in the head (should be a stud in the middle of the bottom of the head) and quickly tap the tab of the driver. There will be sparks. This is normal. Does the chime sound? If yes, replace driver tranny. If no...
Get your meter out and set to 200VDC. Black lead on cabinet ground braid, red lead on each lug of the coil in turn. Should see solenoid voltage on both.
That gets you started...