How do know if the r fuse s need repaced - Arctic Cat 2009 550 H1 EFI 4x4

I suspect you will need a replacement ecu/ignition system and voltage regulator assembly for the battery charging plus of course your blown fuses. But, won't hold your breath but you may be lucky.
Check all of the fuses first.

Jeff, Recheck fuses/relays, probe dash wire to see if you are getting power up to dash, if not then fuse or wire broke. If you are getting power into dash then display is faulty and needs repaired or replaced. Check the attached links,Manuals and guides, Good luck with your Bike
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How to Diagnose Motorcycle Electrical Problems Dennis Kirk Inc
ATV TROUBLESHOOTING AND MAINTENANCE
Service Manuals for Download in PDF

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Here are a couple of posts.
Polaris trail boss fuse box location
This is different year but might help,
http://atvconnection.com/forums/polaris/336771-06-trail-boss-330-a.html

well it tells me that the starter is good and you may need a new relay or it may just be the fuse!! Not sure on that model if that is the only fuse or not, on my 300 bayou there is a fuse at the battery and it could be blown as well. The manual will tell you ALL about the machine and give you troubleshooting tips!!

see these diagrams. 2 different ones

Check fuses and wiring connections also the fan could have burnt out

fuse link should be in the battery cable it's self

sounds like you blew a fuse. also check to make sure the battery is fully charged.