About 8 years ago my sister and I had a computer problem. My friend tried to walk us through it but couldn't. So he asked for our IP addresses and he was able to take over the computer and try some more advanced things. He ended up fixing the problem. Now my sister is living out of state and she's ASKING me for help with computer. I know whats wrong and how to fix it, HOWEVER I tried walking her through some stuff, but she is very computer illiterate. What do I have to get (hardware or software) to be able to take over her computer my IP address? try teamviewer
You could try CrossLoop. I've only tested it in a classroom environment (within local area network), but it seemed to be easy to setup and use. Been awhile, so details are fuzzy, but you don't need to buy, pay, or setup an account if you don't want to. If it seems like they want you to buy or register, look a little harder AROUND the website; because it's not required.

Not sure how secure it is (since they act as the "middleman" to make the connection). Both parties must download, install, and startup the program. Each party gets a unique ID which they need to EXCHANGE with the other party (e-mail, instant messenger, telephone) because each party needs to request a connection to the other party's ID (thru middleman). Look for the installed help file or online documentation.

My mentor (IT instructor) swears by "LogMeIn", but I believe you need to establish a personal account with them (although there's no charge for the LogMeIn Free version).

If you want secure communications, I believe you need to use a Virtual Private Network (VPN) connection. This is something I haven't done yet.
Virtual Private Network (VPN) Introduction

You might want to look at these:
LogMeIn Hamachi2 (VPN)
RealVNC 4.1.3
TightVNC 1.3.10
UltraVNC 1.0.6.5