Attach the painting to the wall using J-brackets. Choose J-brackets with flat backs so the painting lays flat against the wall. Hold the painting up where you want it, and make a mark where each of the brackets should go. Use four brackets, one near each corner, for extra support. Attach the brackets into a stud, or use wall anchors and screws. Slide the painting between the anchors so it is securely in position.
Use specially designed security hangers to hang the painting. These hangers can even attach paintings to ceilings so you can use them on sloped walls. Kits are available that come with brackets that you screw into the back of the frame. However, you don't need to buy the kit. You can find the hardware at your local home improvement store and use your own screws and anchors. Attach a bracket to the top and bottom of the frame to keep it in place. Drill anchors and the included screws into the wall, and slide the hangers onto the screws.
Hang the picture from the ceiling by screwing hooks into the ceiling beams and attaching fishing line to each hook. Use strong, 50-pound fishing line. Attach the fishing line to the back of the painting's frame using small eyelet hooks on each side of the frame. The fishing line will be almost invisible, but the picture will hang naturally against the wall. This works best on walls that are slightly sloped because the painting can rest against the wall, regardless of the angles. Ceiling mounting hanging systems are also available if you want a more permanent solution.