How to make a picture lay flat against the wall when it is hung?

Wire? One thing would be use the blue putty they sell next to glues, can't remember the name, or museum putty on the corners. Or command strips!

If it hangs by a wire, make sure that the wire is rather short so that it hugs the wall and the top doesn't come out from the wall so far. Command strips would bring it close to the wall.

I recommend command strips

There a little rubber/ plastic bumpers for the bottom backside of the frame. I’ve used clear ones, brown ones.

I agree with above comments. Command strips would be best. There are also command hooks but they will not bring it flat up against the wall. Best of luck to you.

If you use the stick-on bumper pads, it allows circulation of air behind the picture (also leveling it) this is helpful in humid climates.