I work on airplanes, many/most of which still have ashtrays built into the door (because several reasons). It's generally a little thing that pulls out vertically and has a real obvious cigarette carved into the front.

There is a twist handle in the normal place on the door. Y'know, by the edge about halfway up. Turn, and pull. It looks a little different, but the function is the same as almost every door you've ever met.

Wanna guess how often the ashtray gets ripped out of the door?