It’s a real shame but there are not many high quality resources for those interested in learning GIS for Archaeology on their own. I have gathered together some resources here (please, let me know if I am missing any).
University of Leicester GIS Training for Archaeologists – decent FREE online course that takes you through the basics. It uses ArcGIS which is a pretty expensive program to buy and it is also base on version 9.1 (newest version is 10.4). Though even watching the videos will give you an idea of the basics of GIS.
There were some great presentations by R Haddlesey that unfortunately are only accessible through the internet archive now.
For more on GIS you can see the chapter by W. Fredrick Limp on GIS and Archaeology in the book Archaeological Computing. This is a FREE book to download. The rest of the book is a great read too.
Oxford Archaeology has developed a manual for Open Source GIS and archaeological survey.
A booklet from ESRI GIS for Archaeology.
Free to Use Software
Before you try to use this software read the resources above. If not you will just be frustrated. They do not hang you out to dry with this software package and there are supports for each piece of software-
international mailing list
international mailing lists
GRASS GIS and Quantum GIS are two programs that you can also download on your own. They also have supporting documantation to help you learn how to use the software- again read the resources above or you might have problems.
A fun package put together by a former? archaeologists (if you ever stop being an archaeologists) is Portable GIS.