Officially your guitar must fit either beneath your seat or in the overhead compartment. If it does not then officially it must be checked in an official IATA approved case.

In practice you are at the mercy of the various ground personnel, gate personnel and flight attendants to bring your guitar on board and to stow it where it is possible to be stowed. Your best best is to keep it in the most compact gig bag possible, not to have (hardly any) other carry-on luggage with you, display your elite tag on the gig bag itself, keep the bag vertical at your side touching the ground, be all smiles and politeness, board as soon as possible and try to stow in the overhead at your seat. If it does not fit in on any flight, politely ask if they will stow it in the closet in first/business.