As long as your neighbor is ok with it, have them move their wireless access point as close to you as possible (unless you want to spend money on a repeater or two). Secure the access point with WPA or WPA2 - WPA2 is preferable - and a decent password that you both know.
Get yourself a wireless NIC adapter if you don't already have one, either variety will do... internal card or USB adapter, and connect to the neighbor's network with the password they gave you.
Edit: This is not illegal, as long as your neighbor knows about it and agrees to let you share the connection. What I would avoid, is advertising that you guys are doing this to your neighbor's ISP. If they have anything in their Terms of Service that says customers are not allowed to share the service in this manner, your neighbor's service with their ISP could be terminated.