I am in the process of laying ceremic tile in my livingroom and I have stairs going down to my finished basement and I do not know how to may it look like it should. I want it to look professional installed.

Schluter systems makes a variety of underlayments, transitions, profiles, etc. One of them is called "Step Rondec" It's designed to be installed under the last tile at the doorway and covers the substrate as well as providing edge protection for the tile at the step.

Schluter-RONDEC-STEP - Schluter-Systems

Another option would be to get a piece prefinished stair nose for hardwood flooring, 3/4" thick, and in the stain you wish, would be installed and the tile brought up to it. tile installed over 1/4" cement board, between the thinset under the board, the thickness of the board, thinset under the tile and the tile thickness will bring you flush with the 3/4" thickness of the hardwood stair nosing.

How exactly did you install this floor?