Another recommendation for TeamViewer.com
Another option would be to use iChat screen sharing. To make it easy, you get 2 free AOL Instant Messanger (AIM) accounts. Configure your iChat with one of the AIM accounts. Then talk your sister through configuring her iChat with the other AIM account. Make each other iChat "Buddies". Now you just select your sister from your iChat Buddy list and request screen sharing. She then gets request to allow screen sharing and you are in business. As a bonus you can also be doing an Audio Chat while working on her system.
There are other ways to use Mac OS X Screen Sharing, but they tend to involve more configuration setup work on your sister's home router.
There is also things like:
Hamachi.com VPN to join your 2 subnets so they look like one local network
The Apple Remote Desktop client is installed on the Mac anyway.
The Bit that does the controlling is the bit that costs.
However the Apple Remote Desktop engine is the bit that makes the Screen Sharing work and is used by iChat to it's Screen Sharing.
Apple Remote Desktop is enabled in Sharing as the remote Management item
This cannot be enable at the same time as the Screen Sharing item is enabled.
To Link in Screen Sharing you need to go to ther Finder's Go Menu and enter an IP.
This IP should be the Public IP of your sister's Modem/router.
That Router should be set to pass data that come of the port for this VNC connection to the Mac she is running.
This would normally be done by setting up Port Forwarding in her routing device, as BobHarris has already said
iChat's Screen Sharing adds a VNC connection to display the Shared Screen alongside an Audio Chat and negotiates it way through firewall and routers (if you can Video or Audio Chat already).
iChat uses a Random port for this and it pays to use UPnP in the routing device at both ends to get it work
(you can't Port Forward a random port and iChat requires 19 other ports to be set up).
Screen Sharing does need to be Enabled in the Video menu of iChat.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously
Is there a way to remotely access her desktop from a distance? The help menu mentioned VNC Sharing and Apple Remote Desktop, but I don't know much about either.
the answer to this is yes. the options others have mentioned are great but you you'd really like to use Apple's screen sharing app all you need to do is either have her plug directly into her modem so her computer is not behind a router OR forward port 5900 to her computer on her LAN. this can be tricky for someone not versed in port mapping on their router but it might be useful to you or someone else so thought i would mention it.
then you can simply use Command-K from Finder to open a new connection to: