I think one of the first important steps is to correctly assess their readiness level so you can respond appropriately. I have a cheat-sheet for myself that is based a model from Management of Organizational Behavior. Responding appropriately helps you avoid lots of the frustration and unpleasantness that can happen. When you are on the phone this is particularly important since it is far more difficult to asses the situation, and respond appropriately then it is when you are working with someone face-to-face.
Encourage them to talk as about the problem as much as possible. Ask lots of questions. You can't see what they are seeing, you can't hear what they are hearing, you don't know exactly what they did to get to the point where they decided to contact you. Uou need to encourage them to tell you what they are seeing, hearing and doing by asking lots of appropriate questions. You need them to be your eyes and ears, and hands.
If you are able then use the tools to remotely view the computer. The suggestions others have made are good. VNC is free but the other options are good too. If you are doing this professionally, you definitely want to work out a good system to remotely support systems you are responsible for.
If you are able, have a computer or VM where you are working that is similar to what they have. If you can't use a remote access tool, then being able to follow along with what they are doing on a different system is helpful. Even if you do have remote access having a VM you can test something on is helpful. That way you don't have to break the real system to try something you are not sure about.
Work on getting as in-depth of an understanding as you can about the computer systems you may support. Some things cannot be remotely viewed or replicated on another system. Some times you are just going to have visualize what they are seeing and doing in your head. The better you understand the systems you support, the easier this is.
As l0c0b0x mentioned see the Your troubleshooting rules? question for advice on doing the actual troubleshooting.