There is a description of the appropriate Groebner basis algorithm in this book:
Franz Pauer, Andreas Unterkircher. Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations. AAECC 9, 271–291 (1999)
I've implemented it in the single-variable case (in the software Regina) and I've been meaning to implement it in the multi-variable case as well. But I usually get too sad to finish – when I look at how inefficient the algorithm is. Some day I'll have it fully implemented in Regina.
The book is quite well written. I find it easy to read.
