you have 3 options..
1) buy a 2 port router and utp cables to connect yours with the router. router would be 5000+
2) buy a wireless router if you dont want to lay cables. now buy a wireles networks card as well.

make sure you secure the wifi connection.
3) if your neighbour has a adsl modem, he'd probably be connecting to the usb port. Now buy only a utp cable and connect your pc with his pc and finally bridge his internet connection to the ethernet connection. This way you can browe internet as long as his pc is ON.
utp - twisted pair cat 5e.
**p.s. - this is important. for options #1 use a straight cable, options #2 use a crossover cable
Cheers,