1) Ensure the wireless module is switched on, and enabled on the laptop.
2) Connect ADSL filter into BT phone socket ( preferably master ) With a single phone, and single RJ11 cable ( This should've come with the TalkTalk package ) - the RJ11 cable needs to go into the back of the Belkin wireless router. It'll say 'WAN' or something like that above the port.
The above should give you 'sync' to your router, as long as there is no problem line side. Most Belkins have a telephone icon, this should be solid green.
3) Now it depends on whether the Belkin default factory settings have the wireless enabled. If it does, you should be able to connect to it. If you're using XP/Vista search for the wireless network ( There should be an icon active on the bottom right, next to the clock with a red cross next to it ) Right click that and select 'connect to a network' The wireless router should be listed in there. Highlight it, and select connect. That should be it.
If the Belkin router doesn't have wireless enabled as default, you'll need to connect to it via Ethernet. When you've done that, go into IE and type 192.168.1.1 ( Or 192.168.0.1 ) - you should get a box popup asking for your username/password, this is the routers default ( usually User: admin, Password: admin or User: admin, Password: password )
This will bring you up with the router GUI, somewhere in there will be the option to enable wireless. When you've enabled that, follow the directions as above to connect to it.
4) When you're setup wirelessly, make sure you configure the router with an encryption key. It'll be inside the router GUI as above. This will make sure the wireless network is as secure as it can be. I don't know Belkin hardware that well, so i'm not 100% sure where security is etc. It'll be something along the lines of Basic/Wireless LAN.
5) Now that you have setup the router LAN side, you'll need to go back into the router ( again 192.168.1.1, or 192.168.0.1 inside IE ) and input your TalkTalk username and password into the router configuration page to tell it to connect - this'll be under Basic then Wan Settings or ADSL, something like that ) When you've done that you should be cooking on gas.
Alternatively to the above the Belkin may have come with a CD, that may do all the above for you

Or the first time you go into the router it might automatically take you through a setup.
To answer your other question, no, you don't need the TalkTalk modem. The router he has bought has a ADSL modem built into it ( by the sounds of it )
Hope the above helps. It's not the best explanation, but it's 20 past 3 in the morning

If you have any further problems, let me know how far you've got and i'll do my best
