What is the best way to get started in this dive?
First, to get started, get started RIGHT.  For example, if you don’t speak Chinese Mandarin already, you should probably start there to first build a strong foundation for Chinese reading and writing.   This way, you can learn more efficiently with Shanghainese, since all you will then have to focus on is the pronunciation and listening (since the writing is all the same). 
Make sure you focus on the tones carefully. If you don't, you will get off on the wrong foot with terrible habits. You will think you are saying one thing when you are actually saying something completely different. 
Don’t forget to practice your Shanghainese wherever you go, whenever you can. Ideally, work with a live teacher every week, so you can practice real conversations.  
As you continue, ask EVERYONE you know (who knows Shanghainese) to correct your Shanghainese. Always. It’s the quickest way to improve--via instant correction. 
Finally, put together a solid study plan and schedule, using the many resources we have assembled for you on the pages to come. So to get started, your first step should be... to go to the next article!