I run two laptops, one with wired access to the internet and the other as a stand alone. I would like to use both computers wirelessly. I have tried to set up a router/modem but couldn't get an internet connection.
My working system is: an HP Pavilion laptop with Ubuntu 12.04lts (Gnome) linked to a thompson speedtouch modem through a Vonage telephone switch. Until I disposed of Windows 7 the laptop worked nicely with a Netgear wireless modem/Router model D1000. But no amount of testing and checking allowed the internet to come live.
My options are: (a) to make the Netgear work with the Vonage and laptop (wirelessly) the prefered option or (b) insert the Netgear wireless router modem but use it only as a wireless router.
I have spent many (un)happy hours working through just about every permutation to make the system work but so far no luck. I have very limited technical knowledge or understanding but can work logically and keep notes of each attempt. Avoids repitition. So any advice needs to be simple and basic without technical jargon. I can follow an instruction.

You mean something like this? http://fruttenboel.verhoeven272.nl/net/apclient.html

You won't be able to do that with a simple WLAN router. A WLAN router is server only. The device needs to have a 'client mode' switch

Hopefully you can follow this Access point guide (which is for Linksys routers, but the basics should/ could be the same for your router)
another link (simpler to read)

good luck

Thank you both for your kind responses. Sadly neither the option of new purchase or the reconfiguration is viable. The first for lack of local supplier, the second as it (and the first response) leave me scratching my head. One forgets that I am new to this and have NO technical competence.

So, you have a stable WLAN signal (laptop 1 is on it). But lapotop 2 is not.

Test 1: conenct a UTP cable between router and laptop 2. Can you now
If so, the network in laptop 2 is up and running. If not you need to run a script to get it working. In Slackware I just edit /etc/rc.d/rc.inet1.conf and issue the command
but Ubuntu will no doubt do things 'better'.

My advice: use fixed IP's to get things running. If all works, you may go dhcpd.

When the UTP network runs, try to switch over to wicd.

When your computer seems to have a dead network, run as root and try again. If the problem is fixed now, it is a matter of privileges (it mostly is).