how to find out if wall is plaster, wood or drywall?
Remove an outlet or switch plate and look at what the edges of the wall are. It should be immediately obvious if they're wood paneling or something. Otherwise, it'll be plaster or drywall. Drywall will have straight edges and a chalky core, while plaster is more organic-looking and flowing, and will have wooden supports behind it.

Regardless, it's actually irrelevant for the task at hand. Your blinds should be screwed into something structural, like a wall stud, and not the wall finish material. There should be a stud up against the edge of the window, right underneath the finish material, so if you drill deep enough, you'll hit it.