For the most part, you can watch Supergirl without having seen any of the related shows (known collectively as Arrowverse titles). You’ll find that whenever a character from another series appears, Supergirl gives the viewers a general idea of who they are and what they want. That said, if you’re looking for the full story, you might want to consider watching Arrow, The Flash, and DC’s Legends of Tomorrow. These titles are usually available on the same platforms as Supergirl so if you have the time (and patience) to watch them all, there’s really no reason not to.