Items Needed

Sponge

TSP (tri-sodium phosphate) either powdered or liquid version

Bucket of water

Empty bucket

Instructions

1. Mix TSP with water according to the package instructions.  Use the "heavy cleaning" formula if available.
2. Throughly clean the wall using a sponge instead of a rag.  Sponges lift off the nicotine rather than push it into the wall like a rag or towel would.
3. After washing a section of the wall, rinse the sponge out in a clean bucket of water. 
4. Repeat this process until the nicotine is off of the wall

If this does not remove all of the years of built up nicotine you can prime over the stained walls using Bin primer made by Zinsser.  This is a shellac-based primer that will seal in both the stains and the odor from the nicotine.