I've not (yet) tried it myself, but recently I read about a 'worm bin', which seems to be a good solution for indoor composting.
The idea is that you have a bin of multiple layers. You fill up a layer with materials, and the worms will do the composting for you. When the layer is full, you add new layers. The worms can travel between the layers because of holes in the bottom. This also makes sure that excess fluids will be drained. This fluid is very potent as well and can be used as a fertilizer when mixed with water (otherwise it's too strong).
After a while, the bottom layer will be fully composted and you can use the contents from that layer, after which you can put it on top to fill it again with new material.
You can buy systems like this, but they appear to be pretty easy to make yourself too.