Glad you enjoy!
In broad strokes, to become an avatar, you must first get marked by an Entity by brushing with it often/significantly enough. Some Entities are easier to encounter than others (eg lots of opportunities for the Corruption through the plot in season 1); if you're struggling to get a rarer specific Entity, you can try spamming visiting the library or Archival Storage during your work day for random opportunities.
Once you first get marked by an Entity, you'll get the option to "answer the call" on weekends, which will list the Entities currently available for you to pledge yourself to if you so wish. Once you've picked one, you can't change to another in this playthrough, but they don't get dibs, so if you get the call of the Corruption super early that doesn't mean that you'll never get a chance to instead pledge yourself to the Eye later on. :) You can also "lose" the interest of some Entities so they might come and go; for instance, you can fight off the Lonely or the Eye by hanging out with your loved ones or refusing to do Institute work.
And once you have become an Avatar, you'll need to regularly feed your patron if you don't want consequences. (But maybe you want consequences? :) )
Playing as an Avatar is totally optional, but it does have lots of achievements and unique scenes (including nsfw -- this is the only way to "date" Entities).