How can I remotely access a computer?

A friend of mine is having computer troubles but I don't have the time to get over to her house and fix it. I have gone through the ruthless trials of Dell tech support and I noticed that you can get a program that, with your consent, allows the representative to control the computer. I have been thinking about that and I wonder if I could do similar to help my friend fix her computer. Also, her computer is broken due to malware. If I was able to access her computer as explained above, would my computer be suseptible to malware also?