How to remotely manage a Mac not on my network?

Question

I'd like to remotely manage a Mac over the Internet. Specifically my mother's iMac, so when she loses Dock icons or can't find her Address book or something I can fix it from my location in another state. Simple things, but trying to explain it over the phone is generally unsuccessful. We're both running Snow Leopard. I can set things up initially on her Mac in person, and then I need something that requires no effort on her end for this to work. Thanks.

Answer 1

As Sijmons suggests, TeamViewer.com might be the easiest solution (and is frequently my suggestion).  This is a secure connection.
Some alternatives.  You get 2 free AOL Instant Messenger (AIM) accounts.  Setup your iChat client with one AIM account, and then setup your Mom's iChat client with the other.  Then you can use iChat Screen Sharing, as long as your Mom is available to approve the Screen Sharing request.  As a bonus, you can text, audio, or video chat with your Mom over iChat.  An Audio chat while using Screen Sharing will allow you to talk her through things while you demonstrate or watch her and provide feedback and corrections.
LogMeIn.com can be used free for personal use (secure connections used), but it does not provide file transfers (you could use something like Dropbox or insync (from Google) to do file transfers.
You could setup a Hamachi VPN (virtual private network) between your Mom's and your Mac (Hamachi.com free for personal use).  Once you have Hamachi setup, you could then just use Mac OS X Screen Sharing.  This is a secure connection.
A more complex approach is setting up your Mom's home router to port forward port 5900 (see portforward.com), then get a free dynamic DNS name from a service such as No-IP.com or DynDNS.org, and run a dynamic DNS updating client available from the service you get the dynamic DNS name from.  Now you can use Finder -> Go -> Connect to server... -> vnc://your.moms.dynamic.dns.name.  And if you also port forward port 548, you can do file sharing via afp://your.moms.dynamic.dns.name (down side is that this approach is not as secure, and it opens well known ports that might be attacked).
And for the really hardcore, you can port forward port 22 (ssh) and then create secure ssh tunnels that you use for screen and file sharing across the Internet.