Get one of these circuit breaker fuse replacements for diagnostic use
http://www.pinwiki.com/wiki/index.php?title=EM_Repair#Electrical_short_troubleshooting_Fuse_helper

Tough to figure it out without seeing it in person. You have a coil that is most likely stuck or a switch that is closed that is requiring a coil to stall pulled/activated. I would check all the stepper units to ensure they are working properly first.....a seized up stepper unit will cause the coil to stick and blow a fuse. Make sure to inspect chime unit coils as it’s pretty common for them to seize up as well.

The part number of the coil may be stamped into the fiber biscuit where the solder lugs are attached.

Went through this recently on a 60 Williams. Try to isolate where the short is -- start by disconnecting jones plugs to backbox and playfield and coin door and bell/knocker and start with just the board in the cabinet (where many coils and relays reside). If that does not blow a fuse start adding back one at a time to see where problem pops up. Alot of this is visual inspection looking for things like solder bombs and loose wires touching metal or other switches.
Yes - you need the breaker to do this as every time you blow a fuse its costly. Use a 5 amp breaker for a 10 amp fuse - you always want something lower. Clay's guide has good info on this as do the other links already noted.
If you have a DMM check that "burnt" coil for resistance - if less than 2 its crap.
Shorts are frustrating and it takes patience and diligence to find them but you will. Start by looking in detail at the jones plugs too as thats where solder or wires can touch each other commonly

If a 100,000 point rollover pops the fuse, I'd go directly to the 100,000 unit to look for a bad coil. In those days, the coil number was stamped into the fiber coil bobbin next to the coil terminals.