How are you connecting to Internet? Via Broadband or Dial-up?
Dial-up to laptop with built-in modem:- use a normal telephone cable.
Broadband via a Router:- use a Filter/Splitter in the telephone socket, and from the filter a telephone cable to Router and Ethernet cable from Router to Laptop. Normal telephone connected to phone-side of Filter.
If more than one telephone in house, then Filter/Splitter needed for each telephone.