My favourite: Waterhouse's Introduction to Affine Group Schemes! It is very friendly and clearly written and gives you the complete basic package on Affine Group Schemes in just 150 pages. With the firm grounding you get from this book you can gather whatever else you need to know (if anything) by skimming through other literature like the books by Humphreys, Springer, Demazure/Gabriel or articles.
For a very down to earth approach with lots of matrix examples, which give you a sense of reality and material for hands-on practice (e.g. while reading Waterhouse), check out Ulf Rehmann's five or six lectures here. Don't mind the unusual introduction - it's from a K-theory school...