Hi. If you would like to try MAPublisher and Adobe Illustrator, I would recommend you to take the MAPublisher training. It is a 2-days course and it covers all the MAPublisher functions so that it will help you when you plan your workflow for your mapping project. Also, if you have any cartographic question and workflow question, your instructors will be happy to assist you with any of your questions
Of course, there are other options to learn MAPublisher/Adobe Illustrator as well. When installing MAPublisher, it comes with 1) Quick start, 2) Full tutorial, and 3) MAPublisher tutorial DVD. Those will help you understand MAPublisher functions when you study them alone.
If you would like to concentrate on studying AI tools / photoshop, like BioGeoMan suggested, taking a class for Adobe illustrator at a local community college and any other training centre is very effective.
Good luck!
Kimi