You have to figure out when/where/how to get vaccinated on your own. Starbucks is providing a letter that verifies you are an essential food service worker, which means in most states you're in phase 1B or 1C. You have to check how the rollout is in your state, and what the process is.

One you get the shot you can put 2 hours for each dose (total 4 hours) in the punch log of the DRB.

On my partner info there’s a vaccine letter “to whom it may concern this person works in food services snd cannot work remotely etc etc” then once you have your vaccine record you just tell your SM and they’ll add it to your hours.
Idk about where you are but Im in Ontario Canada it’s required to self monitor at home and there’s a new form that we need to fill out alongside the Covid coach. I will also be writing “+2 hr for vaccination” there for an extra reminder for my SM.