If you already have a wireless router at your house, then just build one of
these for your neighbor, connect it to a wireless card or USB adapter, and aim it at your house.
I recommend carefully checking your cabling. You'll need a
pigtail which allows you to connect an external antenna to your neighbor's wireless card. If you don't have line of sight (a window facing your house) within the immediate vicinity of his computer, you will need a low-loss
extension cable which will carry the signal from your neighbor's wireless card to your
antenna.
Another thing to be careful about is your choice of wireless card. I recommend getting a USB card for your neighbor rather than a PCI card. This will give you a bit more flexibility in placing the equipment, and will minimize electrical interference. You will need to get a wireless card that is compatible with
NetStumbler.
NetStumbler is used to precisely aim your external antenna for maximum reception. I recommend the
Linksys WUSB11 2.5. There is a newer 2.6 version of this adapter, but you want to get 2.5 because there is an
MMCX jack inside which allows you to attach a pigtail without any soldering.
Good luck with your project!
You can PM me if you have questions.