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.
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. To learn new techniques, I recommend the Online Tatting Class. The website layout is a disaster but if you scroll down on the left hand side you will see the yearly lesson indexes.