EXPERT RESPONSE
If you choose a solution that uses unlicensed spectrum (like Wi-Fi in the 2.4 or 5 GHz bands), then you do not need permission or a license. That's precisely how these bands are supposed to be used. Some other fixed broadband wireless access solutions do operate in licensed spectrum, so steer clear of those.
What kind of hardware to use depends upon factors like the distance between your homes, RF-absorbing obstacles in between you (like trees), and whether you can position outdoor antennas for line-of-sight transmission between your homes. I suggest that you read about wireless outdoor routers to get a sense of what these products offer and the questions you'll need to ask. Here are just a few URLs to get you started:
Alviron BreezeNET PRO.11 Outdoor
D-Link Outdoor Wireless Bridge/Router
Enterasys RoamAbout Outdoor Solutions
ISP-Planet Fixed Wireless How-To Handbooks
Proxim Tsunami QuickBridge and MultiPoint
Wave SPEEDLAN 9000 Series
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