Kids these days. SLRs and range finders were not complicated objects, though I do enjoy your description of "buttons and levers all over it". That appears to be a Canon Canonet Range Finder camera. Not actually an SLR, but more in common with a standard point and shoot. Also, from the 1970s.
Assuming the battery still has any charge, it might actually be worth finishing the roll of film and having it developed. You may want to bring the whole camera to the developing shop though, if you've never removed film from a full manual camera.
The battery is not necessary for actually taking a picture, as that is a mechanical action, but if you had the battery, you'd see a light meter and a range finder overlaid on the view finder.