When connnecting small pieces to other parts, I make a point on the end on the small bit and then insert it into a small hole I've made on the other part, and smooth the edges a bit.
The primary tools I use are a toothpick; a small, smooth kitchen knife; and a saftey pin. I'm looking into investing in some more official clay tools however, to be able to do more precise and detailed work.
Any suggestions for worth-while tools?