I have just bought a new Dell Inspiron One. My first Dell, I want to hook it up in my basement for my grandchildren to use. I have a modem/router (all in one) on my new computer. Do I need a router in the basement and how to I hook it up, I don't have too much knowledge on wires and where they go. HELP HELP! Linda

As long as the older Dell has an ethernet port in back (it looks just like a phone connection but wider with space for a few more wires) You can run an ethernet cable between them (cat5e) for a secure wire connection, and just connect the cable upstairs to the router instead of the PC and run the network wizard on both PC's to make sure you assign the same workgroup name to both PC's. Then their shared folders will be available between them. It would require getting the cable from the basement upstairs and buying a length suitable, but is more secure and easier to setup than wireless.
If the downstairs dell has not ethernet port you can install an internal card for that purpose along with the drivers for it but I bet your Older Dell has it.

I should also mention that if your willing to pay someone, you can have wall sockets mounted and wired between the rooms you want and the router and then use much shorter cords by simply plugging the PC to the wall.

Another thing you can do is if your ISP allows it trade yours back in for a wireless unit. You can get a usb wireless for pretty cheap to connect to the new wireless router and you won't have to worry about where to put the machine.

Search Results for usb wireless at TigerDirect.com (http://www.tigerdirect.com/applications/SearchTools/search.asp?keywords=usb+wireless)

Two things though, Wireless is less secure than wired even when using the latest encryption. And "you wont have to worry about where to put the machine" is not entirely true, wireless has limits in distance and can be blocked or slowed from walls and devices in the home (microwaves are nasty). Most router/modem combos will have a wireless section where you can set it up, check the manual that came with the unit (sometimes on the disk to save a penny).