You will need either a wireless router, which connects to your existing modem, or a combined wireless modem/router. If your 'phone point is close to your desk top PC you can connect the router by using a hard lead rather then buying a more expensive wireless adapter. You will then need a wireless adapter card for your laptop. All the necessary software should come with the equipment. You might consider a usb adapter for your laptop, you can then transfer it to other PCs and use it with them.
I have a netgear modem/router connected to my desktop by hard lead. My wife and son have wireless adapters on their PC s and connect to the internet wirelessly in different parts of the house.