Much of becoming a good Role Player, will be a result of trial and error, and with multiple efforts you will find the style and technique that will suit you.
A couple of important things to also keep in mind in regards to RP. First, and i think this is a common error many people make, (I included) don't get impatient. Don't emote for the other person(s).
One other thing to keep in mind, if you are in RP and you need to converse about anything not directly in the RP itself, then bracket that text so the other player recognizes and realizes what it actually is. Some people use a single bracket and others use a double bracket. ((this is a sample of a double bracket))
It is my hope that this offers you some aid in becoming an accomplished role player; after all, the next partner I may role play with could be you.