It's hard to say without referring to the manual. There may be a way using a public, guest, unsecured network but I don't think that's a good idea.
You really should be using a password or else your entire network is not secure. Then you should have no problems with piggybacking or hacking:
1) See your router/gateway manual and access its settings via your PC browser.
2) Enable one of the secure networks that all your wi-fi devices supports (WPA WEP2 etc.). The higher the better.
3) Write down your USER NAME and PASSWORD.
4) Activate the Range Extender.