Is it the case that to set up a wireless network I need to replace my old modem and have this router connected to the phone line and then have the router connected to the desktop via an Ethernet cable and then configure this to my computer and then once set up the laptop will pick up the wireless signal?
Yes, that's the way forward.
You should find that your Netgear router comes with a "quick setup" guide which is easy to follow ... connect the router to the phone line and to the desktop via the Ethernet cable and get that part working first.
Once you can access the internet from your desktop then go through the steps of setting up the wireless link to the laptop. Remember to encrypt the wireless link using WPA-PSK (rather than WEP which is less secure).
RC