Just buy a repeater that has a built in switch, or better yet buy a basic Linksys WRT54G router. You can change the mode to "Repeater" and enter the network details (ESSID aka Network Name) IF you load the custom Firmware that the instruction website below lists.
You can then set up the repeated network to use encryption which should be WPA or WPA2. WEP can be cracked in no time by an amateur. The WRT54G is a router so you can also run network cables to any physical LAN devices as well assuming your neighbor doesn't wise up to the situation; which if they left their network with no encryption they will not.
Here are instructions some other jackass wrote: http://drgigdidit.com/wifirepeater/
Funyuns out.
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