Once you wash up on the shores of Aeternum you’ll be guided through a series of beginner quests on the beach. You will need to complete those quests. If you do not complete those quests you will not be able to access the quests in town. So, do not skip these.
Once you complete the first few quests you will then be directed to the closest town. You will need to continue to progress through the quest line and you’ll eventually be directed to your first faction leader for a series of a faction quests. Once you have completed the faction quests for all 3 faction leaders you are then free to choose which faction you wish to join.
If you want to see the series of quests you’ll need to complete based on which starter area you spawn into check out the quest database here.
You must reach level 10 (which you will by completing all the quests) and have completed the applicable quests to then have the option to choose one of the 3 factions.
Bear in mind that once you choose a faction you are then locked to that faction and will not be able to switch.
If you wish to play on a different faction you will have to start over on that server or join a different server.