Use Command hangers.
I believe this is a duplicate
Get a wooden paint stir, but nail part way through near the bottom place the picture on the naillift the stir until picture is where you want it, push until it punctures wall remove everything and place your nail in the punctured spot. If it’s a bigger frame make sure you have help, put it as above, have someone remove picture, and still holding stir in place, push nail in to mark.
Depending on how much the picture weighs I would try Command Hangers.
If you don't wan't to put any holes in the wall at all, your best bet would be to use Command Hooks, like Mogie said. Just make sure you check the weight restrictions and follow the directions.
Check out the 3M Command hooks and get the correct size for the weight of you picture. Do not hang your picture too high as most people have a tendency to do. Keep the center at eye level.
Command Strips are incredibly easy to use. They stick to the back of your picture frame and adhere to the wall.