Obviously, the minimum requirement to use VoIP is a connection to the internet. If your connection to the internet is through a standard dial-up modem, you will also need a computer to access the internet. Keep in mind that a dial-up connection, can only provide a maximum of 56 Kbps in bandwidth, which limits the quality of VoIP services.
Ideally, you will have a broadband connection to the internet, often provided by a cable company, DSL or a T1(E1) line. These kinds of connections usually provide sufficient bandwidth and more than enough to be able to use any VoIP service there is with an acceptable quality. If you wish to use your VoIP phone just like any normal phone, it is best to have an "always-on" broadband connection: one where you do not need to log-in to be connected. If you have a broadband connection, adding a low-cost router or gateway can even turn an internet account that requires log-in into an "always-on" account, as the router or gateway ensures a constant connection.