With most access points, Wi-Fi equipment and standard 2dBi aerials, they will only operate up to about 100 metres (~110 yards) apart with clear line of sight. To extend this range, your neighbour will need a more powerful aerial for its PC. I would suggest a directional high gain aerial and locating this in a window facing your house. A typical Wi-Fi aerial included with most PCI cards is 2dBi. For every 3dBi increase, the reception and output power doubles for a directional aerial. Unfortunately, if they are using a laptop, USB Wi-Fi card or a Wi-Fi connection where the aerial cannot be detached, this will make it more awkward as most laptops don't have the ability to attach an external aerial.
For your own Wi-Fi access point, try placing your Wi-Fi access point in a Window or area where it has clear line of sight with your neighbour's house. A Wi-Fi signal does not penetrate walls very wall, especially if you've a concrete or brick outer wall. Another tweak would be to replace your Wi-Fi access point's aerial with a more powerful one (e.g. with a 5dBi or higher omnidirectional aerial) and make your the Wi-Fi strength in your access point's configuration is set to max (if this can be changed.)
With two directional Wi-Fi aerials, I've already seen someone with success connecting their house to their office network about 500 metres (~550 yards) apart using two Wi-Fi access points in bridge mode, which give them fast access to their office network from home.