Tsuri-Goshi's key points:
a) Grab uke's belt. You can do this over uke's right shoulder, under her right armpit or over her left shoulder (Georgian Grip).
b) You will need to pull uke downwards in order to get that belt grip. Don't attempt to throw uke until uke tries to stand upright again. This will give you the space to come in.
c) Switch your right hand grip from uke's lapel to her sleeve if you feel you need more space to enter into the throw.

Tsurikomi-Goshi's key points:
a) The kata version is a complete waste of time.
b) The modern version involves a high grip. You can grip anywhere along uke's back but if you grab the belt, it becomes tsuri-goshi. (This modern version is recognized by the Kodokan as a form of tsuri-goshi).
c) Other than the grip, the mechanics of this technique is identical to tsuri-goshi.
d) Switch your right hand grip from uke's lapel to uke's sleeve if you need more space to enter into the throw.