Life between deployments can really vary. It depends on what your squadron is doing at the time and your groundjob within the squadron. Did the squadron just get back from deployment? Or, are you working up to go?
Generally, getting ready for deployment, "works ups", are the busiest time. Work ups can be quite painful. They are a series of mini dets to the boat and to fallon. Usually for only 2-4 weeks at a time. Your squadron adapts a sort of nomadic lifestyle. At the same time, you are under the microscope from various sources to make sure that your squadron gets to a certain "readiness level". You achieve this readiness through completing different missions and types of flights on a complicated matrix. That sounds cool, and it is good for the logbook, but you will learn that there can actually be such a thing as "too much flying". You also begin to work more with the rest of the airwing and other battle group assets. It is cool to be part of your first big 20+ plane strike, but you must also help in marathon 12 hour strike planning sessions.
After you return from deployment most squadrons adapt more of a shore duty mindset until work ups start again. Some will go down to 4 day work weeks for a while. Other than night flights, you will generally be on 8-16 type day if your ground job is not too bad. That annoying readiness matrix does not completely go away, and you still fly a variety of missions. There is also in house unit level training. Everything from sims, wingman specific flights, section lead training, etc. For VFA at least, you should leave your first tour with a bunch of quals- level 2,3,3I,4, FCF, etc. The oversight for these comes from the weapon school, but is mostly instructed by the senior O-3s and O-4s within the squadron. These briefs and debriefs generally take a while. There is also a lot of random tasking that comes down for squadrons back from deployment. Everything from VIP visits, to flybys, helping out FACs with CAS training, flying Orange air for airwings working up, etc. They usually sprinkle in a couple of good deal dets to fun locations like alaska or key west.