Here’s a good MIgardener video showing how to sift through your compost heap.
His pile is clearly past its thermophilic phase, as it’s cooled down enough that it’s filled with pill bugs and earthworms…these are the critters that turn your material from compost to finished compost, by further breaking it all down. This phase is essentially as long as you want it to be.
His trick with using the pitchfork to separate out all the twigs and non-composted material seems to work well for him. I made a compost sieve for screening mine, but a pitchfork would make a great preliminary screening as well.
He mentions nutrients leaching out into the soil… a simple method for helping prevent this is to start your compost heap with at least six inches of brown materials such as straw, hay, shredded leaves. This is your “biological sponge” that will help keep everything retained.