[NBLUG/talk] How to access my home computer remotely

[Roger House]

I'm currently running Ubuntu 10.04 on my computer at home, and I'll soon
need to access this computer from sites away from home.  I'm hoping that
the access from afar will allow me to drive the home computer more or less
as if I were sitting in front of it.  I will probably be using a laptop 
when
away from home, and it may be running some version of Windows; I do not yet
know if I will have the option to run Ubuntu on the laptop.

I would very much appreciate detailed instructions on how to go about this.
Of course, I'll need to leave my home computer running when I'm at a remote
site.  But, what programs should be installed on the home computer?  What
permissions should be set up so access from a remote site is allowed?  What
software is needed on the remote laptop?  How do I make the connection from
the remote computer to the home computer?  Will I have issues with IP
addresses?  I use Comcast with a cable modem and a router.  I know the 
router
provides a local IP address for the home computer, but it seems that the
remote computer needs more than this.

Any help will be appreciated.  Don't worry about saying the obvious.  I'm
essentially a network newbie, so no explanation can be too simple to be
useful.

Thanks,

Roger House
rhouse at sonic.net