How to program router for Remote Access?

It depends upon the exact model of your Linksys router.  See this page for detailed instructions:

http://www.portforward.com/english/applications/port_forwarding/RemoteDesktop/RemoteDesktopindex.htm

Connect to your LInksys Router.

You can do this via web browser and the web address would be http://192.168.1.1
as long as the default settings are still in place.

Login using the admin account and whatever the password has been set to.

Go to "Applications & Gaming"
For the application name type in something descriptive.
Start and End ports should be set to 3389
Set the protocol to BOTH
Select the IP address that the computer you want to connect to it set to.

Hopefully this helps

Your need is a bit unclear, but I think what you are asking is how to connect a satellite office to a main office.  Please correct me if I am wrong.

The general way to connect a remote site is using a site-to-site VPN.  Ideally, you would have routers from the same brand at each site, that offer site-to-site VPN connectivity.  You then configure the VPN in the routers.  This setup varies by vendor.  I've used Netgear FVS-xxx models for inexpensive setups, but I usually use SonicWALL firewalls because of the many additional features that they offer.

This VPN configuration allows the satellite office to access resources across the internet as though they were plugged into the same network.  However, speed to database applications will usually not be adequate, so they usually require a terminal server connection.  Let me know if you need that kind of connectivity, and I or someone else can elaborate.

Regards,
PfSC

Also, make sure to turn off your Windows Firewall or at least have it set to accept traffic from port 3389.

My situation is this.  I have a computer that I sometimes want to connect to.  It has a DSL modem connected to the linksys router that also serve as a lan hub for the three machines in the distant site network.  I want to set up an icon to click so that my machines, a laptop with wireless connection to the internet also througyh a linksys router, can connect to the distant machine so that I can access and run programs that are resident on the distants machine.  I want to be able to connect from different locations, sometimes in a motel room, sometimes from my home, and sometimes from within my office behind the router which connects my machine and several others in a local network which is connected to the internet through DSL or cable modem that is connected to the  local router also serving as the hub for the lan.

I hope this clarifies the  unclear matters in my original description of the question at hand.

Over all, I am looking for a step-by-step instruction that allows me to set up the two ends of the connection and then to use them from time to time when the nedds arises.

JLBlake

And for instruction on Remote Desktop from MS, here is the link: http://www.microsoft.com/windowsxp/using/mobility/getstarted/remoteintro.mspx

JLBlake, any feedback?

I working on trying it out.  I will have a chance to try it this week.  More feedback later.  

JLB