David,
Anita Grossman Soloman at Make it Simpler has lots of good ideas but a really good way to start out is not to try cutting 22 inch strips. Fold your fabric in half again or just cut it so you aren't working with such long strips. Then your ruler won't slip on you so much. Simply Quilts- Alex Anderson also shows you some helpful ideas about squaring up the fabric. Go to Leah Day at
http://www.daystyledesigns.com/, she has some helpful videos for free.