Aerate. Your compost needs oxygen if it is going to break down the materials you add. If it's a tumbler, turn it. If it's static then get a stick/pole/shovel and get in there and move it around.
Save the worms. If you find a worm while you're gardening carefully relocate it to your compost bin. And it will happily work on breaking down your wastes. The more help you have the better!
Go Big. Container wise that is. Bigger is better when composting but smaller is better than nothing at all.
Get cracking! Rinse and break up your egg shells before adding them to your compost pile. This gives them a head start and you will be less likely to find undigested shell later when you go to use your compost.
Add fluid to your compost. You don't want it too wet but you don't want it too dry either. Water-downed leftover fruit juices are a great treat for your compost instead of pouring them down the drain.
Sunshine is best! Composters work quicker in sunny locations but if you have to, partial sun will work too (it'll just take longer).
Cover it up. Keep a clear bag of leaves next to the composter so you always have brown material to cover new waste additions. This will also help keep the fly population down in the summer.
Double duty. If you have the room, two composters are better than one. While you are busy filling one composter the second one can be busy working in the sun. When it's time to empty one they can switch positions and start all over again.
Cupboard list. Keep a list posted on the inside of one of your cupboard doors so you can see at a glance what can and cannot be composted so there is no confusion.
Brown shredded paper will help absorb odors and juices.