When you've got anything, add it to your active pile.
When you start out you'll only have an active pile. In time it will fill, heat up, collapse down, get more added, rinse, repeat, etc. Eventually, it will fill and stay full. That's when it's time to set up a second one. Maybe a third one in time. I have 4 because 1) I'm lazy, 2) I've got the space, 3) I'm not in any kind rush (and you can't be if you're #1 lazy) and 4) I compost all the no-no's like manure from meat-eating animals, branches of poisonous things like oleander and (god help me) chicken carcasses. These #4 items need to be composted at least a year before they're completely safe to use again.
When you go back to the first one and you can't get it to heat up anymore by turning it or adding water it's time to break it down. Remove or loosen whatever you've got surrounding and containing it. I get a seat, a cold drink and set up my dumping wagon with a hardware cloth sieve on top. I load in a few shovelsful of my compost and sieve out the uncomposted stuff. That I add to my most recent, most active pile. When the wagon's full, I take it to the spot in my garden that can use a little rejuvenation and dump it on. This is when I'm setting up my newest pile again and that's where I put the really big stuff that it's clear will need all the time it can get. Happily, if it's already come from a previous pile, it's loaded with all the micro flora and fauna that inoculate the new pile and get it ready to start digesting what follows.
Lots of people don't bother sieving it out but I'm a lazy composter and I'm not careful that what I throw on the pile is in small pieces or doesn't have any colorful plastic printing coating the cardboard or will break down in a single run through the pile. I take care of that stuff on the back end. Some things like bones, large branches and roots will go through 3 or 4 piles or even more.
So, to sum up, eventually you'll have a finished pile ready to go back into your garden, a pile that's full but still breaking down/heating up and a pile that's still accumulating waste. This is the conventional 3-bin system you may read about. Not necessarily the required way for everyone but an efficient system that's been developed by generations of gardeners.