There are quite a few systems that employ Internet Linking for International coverage. EchoLink, AllStar and IRLP are all available to Licenced Amateurs worldwide and may be accessed either directly, using a node or computer or by an Internet Linked repeater.
EchoLink is perhaps the longest established system and has thousands of users all over the globe. When you register for the service, you are given a node number, which is your identifier for the network. The concept is very simple - find a user/link or conference and connect to it in order to make contacts.
There are two ways to connect :
As a User with a PC.
The PC is connected to the EchoLink server and you use the sound card to make the QSO. Simply connect to the user you wish to communicate with and using the keyboard (usually the space bar) as a PTT with the on board mic and the PC speakers for audio. There is also an Android App for use with a smartphone or tablet.
The other way to connect is as a SYSOP, which involves using a node radio connected to the computer with an interface, which in turn is accessed with another radio (usually a handheld).
AllStar and IRLP are accessed in similar ways with only subtle differences. All methods are accessible via a repeater that is suitably equipped, Repeaterbook is a great Android App for finding a repeater to use. Access is gained by entering DTMF tones for various functions.