It may work differently depending on your location and number of referees on the league.
Where I am, my local county league is the Cheshire League, which is where I started refereeing open age football (bit late to the party, starting at 29 - but it’s a league I was familiar with having played in it for over 10 years and no appetite to do junior football)
The Cheshire League has 5 divisions, with the Premier Division being a Step 7 feeder league to the NWCFL (so has L4 referees with NARs) - the other 4 divisions have solo referees and you can do any division as a L7-L5.
I started by being given lines on the Premier Division, then introduced to middles in the Reserve Leagues - usually 2 of each a month assuming a month with 4 Saturday’s and available for all.
Once I grew in confidence and experience, having had feedback from L4’s and other experienced assistants (plus a couple of Observers) - I then joined the NWCFL as an AR, giving one Saturday a month to them, plus midweeks and the remaining 3 to Cheshire.
As was earlier mentioned, you’ll need to be on the ball with admin if you join the NWCFL - closed dates in 2 months in advance (e.g. December closed dates would need to be submitted by the end of October) and you could be appointed to a game on any given day that’s open (even at late notice) - if you can’t do a game you’re appointed to or need to close a date after the appointments are out, you’ll need to have a good excuse - it’s semi professional football so admin needs to be spot on. If your date is open and you’re given a game on a Friday afternoon for the Saturday, saying you have a game on another league won’t be deemed a good excuse and they are also entitled to cite Order of Precedence.
NWCFL is a great league with some brilliant clubs and grounds - but it’s definitely not for the feint hearted or in my opinion, a place to be dipping your toes in to open age football for the first time and learning the initial ropes of running the line - up until a couple of years ago you had to be a L5 to be an AR on the league, I believe it’s only fairly recently it opened up to L6 & L7.
However, once you’re there, the experience you’ll get and amount you’ll learn are second to none.