You have two choices. Either get an ADSL router and replace the TalkTalk beast with it, or use Internet Connection sharing. This will involve having more than one ethernet adaptor on your PC. You plug a wire from one ethernet socket into your TalkTalk modem, and a wire from the laptop into the other ethernet socket on the PC. You can then configure the PC to share its internet connection with the laptop.
Getting a second ethernet adaptor is as simple as buying an ethernet card on
ebay or the like and plugging it into one of the expansion ports on your PCs motherboard. Only go this route if you are comfortable mucking about with the innards of your PC.
Personally I think getting a new router with more than one ethernet connection would be the best option as the other one may be a little cheaper but a lot more faffy. Get something like this:
http://www.ebuyer.com/263577-tp-link-adsl-modem-router-4-port-switch-td-8840t
It's called a router because of what it does to data that is sent to it. If you have more than one computer on the network then when a computer sends requests or data to another one, the router works out if the data should be sent to another machine on the network, or down the ADSL connection to your internet service provider. Therefore the router "routes" the information by deciding which route to send it and then sending it on its way. Once at your ISP their big scary expensive routers "route" the information to other ISPs and eventually to the correct destination.