I'm very much a novice tatter so rather than tutorials written by me, this section of knitting-and.com houses my collection of vintage and antique tatting patterns that have fallen into the public domain.
If you'd like to learn to tatt, Craftsy have an excellent class that teaches you the basics of suttle tatting and includes several patterns to get you started.
For instructions on learning to tatt I recommend The Complete Book of Tatting by Rebecca Jones. I used it to learn the basics of tatting and found it very useful and to learn new techniques, I recommend the Online Tatting Course
Tatting for Experts and Beginners by Semco. Semco Instruction Book No 16.