The SCA prides itself on encompassing most aspects on medieval (and earlier!) life, in as much or as little attention to detail as you desire. You can start by putting on a tunic and seeing what we do. From there, you might be interested in heraldry, combat, or the arts and sciences (medieval craft). You might like to do all of them.
You might find you want to dabble, or you might fall down the rabbit-hole of research and create something authentic and documentable to a specific time and place. How you recreate is up to you, and there are people who are willing to help you on your journey no matter how detailed you want to get.