NAT is a standard feature on your typical home wireless router. These devices usually have four ports for wired computers, and can be configured to broadcast wirelessly with a range of roughly 50-100 meters, depending on interference from walls and other objects. Most modern ones will be outfitted with WEP and WPA2 encryption methods for wireless transmissions. Even if you do not plan on using wireless access in your home, this device will still suit your needs. You are not required to allow wireless access by using this device, and it will not be configured to broadcast by default. This wireless router is an example of the kind of device you will need.
When plugged into your cable or DSL modem and properly configured, it can broadcast wireless Internet to your entire house, and will often even reach your neighbors. Fortunately, it is fairly simple to set it up so that only the people you want to can use your Internet connection, and no one can view your personal information.
A wireless card, either already integrated into your laptop or desktop, or installed in an expansion slot, is needed to receive the wireless signal being broadcast. Modern laptops are nearly all equipped with wireless receivers, but most desktop systems are not. If you cannot have your wireless router in the same room as your desktop system so that you can plug it in with a cable, you can use a wireless receiver expansion card like this one. This kind of device is installed in the PCI (long white) slot on your computer's motherboard. This article gives detailed instructions for installing an expansion card.
If you simply do not want to deal with an expansion card for receiving wireless signals on your desktop computer, you can instead opt for a USB device like this one, but you will pay a bit more for it.