Well, in its simplest form you need some sort of communication device, which may be a softphone or a physical device such as an IP Phone.

There are various ways to set up communication between two or more parties.

a) Peer to Peer: Does not require an in-between, i.e. communication is established directly beween caller and callee. You need to know the IP address of the recipient of the call and the recipient must be connected to the network and have a suitable device (softphone or physical IP Phone) ready to receive the call. 

b) VoIP Service: Usually you need to sign up with a provider, though some ISP's offer that nowadays as free or paid add-on to their internet connection service. They may offer a presence service for other subscribers to see if you are online or not. They usuall also offer PSTN termination services so you may call any regular telephone number anywher in the world using your softphone or IP Phone. It pays to do some shopping when selecting a VoIP provider. Charges vary greatly and wildly. Check elsewhere on this site to find the ones wehave experience with.