First of all make sure your ssvs and sm know that you are interested. Also ask how you can help your ssvs with some of their responsibilities and if they can explain what how and why things are done... I often let some of my interested and responsible baristas do some of the typical supervisor tasks like milk counts, temps, helping with pulls or inventory counts. I even sometimes let them be a temporary play caller so they can get a feel for how it works. Obviously I supervise all of this and if it gets crazy I grab the reins, but it helps them get a feel for if they really want to pursue the path, and honestly helps me out if I have a lot on my plate.

First comment was really everything you need to know,but also if you are able, let your sm know that you are willing to transfer. You can even look on taleo and see if there are any available shift positions open nearby, and just apply.
If your not a barista trainer yet you should also get certified in that as well.