Levels are controlled by experience points [XP] gained
This
how-to-earn-experience-in-planet-minecraft is somewhat out of date (notebly getting an emerald [3XP] is not listed) but I've not found anything more current…
Basically, one gets XP either when one posts (threads, replies, or 'content' — but not wallposts) or when other interact approvingly with one's posts/content (e.g. by giving emeralds, replying, liking/favoriting, downloading, etc.)
Something to be aware of: the update to one's level is not always instantaneous, but may take a few minutes [e.g you may not switch to level 2 in the same second you pass 285 XP].
With that caveat, the process is automatic [Nothing similar to the AD&D version :D .]