Shizuka teaches Hachiman's Japanese class and also handles guidance counseling—basically she's supposed to help him figure out his future. She clocked his whole "loner with problems" thing pretty early on and decided the best fix was forcing him into the Service Club, which definitely seemed like a choice at the time.
Beyond the job description though, Shizuka's kind of a mess in her own way. She smokes, which is already weird for a teacher, and she gets weirdly defensive if anyone brings up her age. She's also constantly quoting or reenacting scenes from shounen manga like it's the most natural thing in the world. Oh, and she has zero respect for doors—she'll just barge into the Service Club room without knocking, which absolutely drives Yukino crazy every single time.
Content compiled by AnimeList.moe from publicly available sources.