Anaerobic compost is foul stuff and a condition to be avoided. To my nose, it smells like a poorly run dairy operation and that isn't something I want replicated outside the kitchen door.
We have a snooty Smith & Hawken composter, which my wife picked up for free at a demo several years ago. Prior to that, I always used wooden pallets as walls for compost. I have a sort of corkscrew aerator I ordered from a small manufacturer in Arizona. I used to just attack it with a turning fork, but this is easier, so I use it more frequently. That's a good thing.
Lots of leaves go into our compost, as well as all the kitchen scraps, coffee grounds, etc. A year ago, we bought a giant bag of crushed corn cob for a rabbit's litter box before learning it's dangerous stuff. So I added it to the compost and the pile has worked beautifully ever since. I'm now putting cat litter in too now. The cat litter is recycled newspaper pellets.
Every year I remove most of the compost and bury it in the area where I dump other dirt I dig up here and there. It's my topsoil factory.