2005 king quad 4x4 Suzuki smoking issue
 

Where to start on Suzuki 2005 4x4 king quad smoking issues

A 2005 would make it a 450 or 750. The 750 has a plated aluminium bore so you can't rebore it. With any engine, just take the top end apart, find out what is worn, and fit any new parts it needs. It may just need valve seals, but the head has to come off for that anyway.

Is the smoke grey/blue or black?
My understanding is black is a fuel air mixture problem and blue is burning engine oil.
is it consuming engine oil?
I suppose a compression test might give you some clues as well. You can pick up a compression tester fairly cheaply.