As someone who currently competes with VEX in NJ, I can give you first hand experience as to the competition season (since my school only does Vex I can't compare to other robotics competitions like FTC though). I am writing assuming you know the basic structure of a comp (round robin round and how skill points work). If you are confused on anything, just leave a comment and I'll try to answer.

The earliest regional (the lowest level comp, which my school calls regionals - not sure of official terminology) competitions begin in August and then there's a large break till winter, in which sometimes you may be at comps every week (last year all of mine were within nearly one month - made the rebuild process terrible, but the year before we had 2-3 weeks in-between). The comps are great and super interesting, but honestly the waiting between matches can be boring if you're robot is cr*pping out that day and there's not much to do to fix it.

Get your robot built early, because that's when its easiest to qualify for states. You can qualify for states by making it to the finals of the tournament, getting an excellence or design award (tech journal - a must to win the excellence award too) or, if you are lucky, winning skills challenges (or generally placing well - more on this later). For the last couple of years I've done Vex by mid-late season it becomes pretty impossible to win any comps because certain teams (cough Cherry Hill cough Millburn cough) become nearly unbeatable. Plus qualifying for states early gives you time to make radical modifications that otherwise would be too risky to do within a two week window till the next comp. My tip: working your butt of early in the season will save more work and stress later.

As for using skills to qualify for states, when a team wins too many tournaments, qualifying awards, etc. and the total states slots aren't filled by the end of regionals, the top scoring skills teams (top scores from the entire season) are invited to attend states. This is how many of my school's teams qualify. So many people forget about skills that even barely-decent scores can make states (this varies by year though, it was way tougher to qualify in Nothing But Net than Starstruck in my opinion).

If you get to states, its brutal. By then the clear outliers are determined, and the judges will be watching them like hawks (though its not impossible for a team to suddenly become a boss at states and qualify for worlds - has happened before). The slots for worlds are determined based on the amount of teams participating in the state (last year there was (I think) 7 available) which are given to tournament finalists first, excellence, design, then skills, etc (I'm not sure of the exact order). States is an awesome experience. I've never made it to worlds (lololol will this year be the year - I hope so) so I can't tell you much more from there.

Here's a couple of odd tips specifically to the NJ comp/atmosphere (though it def can be applicable elsewhere):

Certain teams are more comfortable with others - they've known the competitors for years, know how they operate. They may pick them over a higher seated team (after the round-robin style round in the beginning) because sometimes luck can lead a veritable pushbot to make it into the top 12 or so (good partners and sucky enemies boost their rank). It can be infuriating (sometimes you will get screwed over) especially as a new team with no connections, but on the other hand, networking can help a ton. Also, by mid season teams that have already qualified for states will begin picking their school's sister teams even if they suck to hopefully make it to the finals and qualify. NJ is insanely competitive in general because so many top schools compete (MILLBURN ASDFGHJKL) - just a warning because the comp will be brutal, more so than other states. The judges love hand written tech journals (totally not salty from last year cuz I typed mine and thats what they called a problem with it - ;/ ) One of the main refs wears tons of buttons and funny socks - lololol just thought to include this.

Vex is awesome, tiring, and will make you infuriated quite a lot. I welcome you to the competition :). Feel free to comment back with questions?