The program is installed, you've logged in successfully, what now? I would start by adding contacts that you want to send instant messages to: go to Contacts > Add a contact. Input at least the e-mail address of your contact, and click the "Add Contact" button.

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With Live Messenger, you can indeed do much more than send text messages: do video conferencing, make voice calls (to a PC or to a phone), share folders, and play games, just to name a few. The menu bar has an additional item right next to Help: Plus!, a freeware which does not originally come with Live Messenger. This is a neat little add-on that really extends the functionality of Live Messenger, with interface skinning, enhanced logs (organized & searchable conversations/events), simultaneous use of multiple accounts, etc.