Quests come from people. Somebody in the world wants something done, and you get the job by walking up and talking to them.
Find somebody who is asking
A marker over somebody's head means they have work. Walk up and right click them, or hold your thumb on them if you are on a phone. If they have something for you it is in the menu that opens, and their offer says what they want and what they will pay.
The first jobs are in town, a short walk from the quay.
Take it, then follow it
Once you accept, the current step shows in the corner of the screen with how far through it you are.
A line of markers points across the ground toward wherever the step wants you to go. If you would rather find things yourself, turn the trail off in the settings and the journal will still tell you where to look.
Open the journal to see everything you have taken on, what is left of each one and everything you have already finished.
Work that comes back
Some people have standing work: thin out the monsters in a forest or a mine, come back tomorrow, and do it again. It pays every day, which makes it worth doing on the way to somewhere else.
If you change your mind
Abandon a quest from the journal and go and do something else. Coming back to it later costs you nothing.
Next: your first dungeon.