What stage are you in?
Step one should be talking to the senior Marine in your squadron. Half the battle is getting accepted by the Marine Corps, but also half is getting released by the Navy. In the past, you would swap services, continue flight school, wing and then attend TBS prior to reporting to the FRS.
Be prepared to take a PFT/CFT and crush it, and be prepared to explain why you want to make the change without putting down one of the services. I.e., not "I want to be a Marine" not "I don't like the Navy."
Be prepared for a "no" as well. To Big Navy/USMC, SNAs are numbers and not really people. You've been counted as a Navy bean, and they may be reluctant to let you go based on their manning numbers.
Also be careful about assuming the grass is greener. I love being a Marine Aviator, but the quality of life and demands are different from USMC to USN. Flight school is representative in some ways of the USMC culture, but in others is a pretty idealized version. Swapping to USMC has implications not just for platforms and deployments, but also for B-Billets and career timing.
Ask your Marine IPs what they liked/didn't like about their communities. Keep in mind that, frankly, the Marine Corps generally does not send it's rising stars to flight school as IPs. There are great Officers and great people there but think critically about what they say. The fleet also probably looks a lot more fun a year or so in the rearview mirror.