The premise: shy, lonely automotive nerd but genuinely nice person Keiichi Morisato tried to dial for takeout food one day and instead got the Goddess Relief Office, where the First-Class Goddess Belldandy answered his call and granted his wish. That wish was "I want a goddess like you to stay with me forever."
In the first volume (which is absent but we'll visit in a clip episode at some point), Keiichi and Belldandy have fumbled towards a romantic relationship at a slow pace but one they're both comfortable with. This has been thwarted to various degrees by interactions with Keiichi's sister Megumi (called "Aki" in the subs because huh?), the members of Keiichi's college club, the Nekomi Tech Motor Club, and Belldandy's sister Urd, whose JFA attitude really isn't helping things much.
We now join Ah My Goddess, already in progress.
(I apologize for nothing)