Navigate to the game menu. There you will find an entry called "Alliance". Clicking it you will see the entries "Alliance List" and "Team-Seeker". The Team-Seeker tool allows you to find alliances that are closest to your chosen playing area, while the alliance list shows all existing alliances sorted by their net credit worth.
Remember to read the presentation text, before you apply to a certain alliance, since a lot of alliances have requirements you have to meet before they consider your application.