Make sure that the hooks on the back of the painting are fixed at the same height. Sounds logical, but it often goes wrong here. You think you can do on your feeling alone... Yes very good, but just grab that measuring tape anyway. After all, you do want your painting to hang straight. 

With a thread or not?
You can hang a small painting with a thread. The advantage of this is that you do not have to attach hooks at exactly the same height. You can move a thread back and forth a little to determine whether the painting hangs straight.

Do you have a large painting?
Then use hooks instead of a thread. A large painting (especially if there is a frame around it) is heavy and the chance that a thread will snap is therefore high. A painting also shifts position quickly if you touch it while cleaning or walking past. A large painting stays hanging well with hooks.

Good screws and plugs
Use proper screws and plugs. This sounds simple. However, it is so important to use the right screws and plugs for the wall. Are you in doubt? Then visit the website of a hardware store to see which plugs are suitable for your wall.