Leveling your focus schools is done by acquiring focus points. Focus points can be acquired via focus lenses, which drop as bounty rewards from the Plains of Eidolon (alternately, these can be traded for from other players, and/or purchased off the ingame market with platinum).
Once you have a focus lens, apply it to a piece of gear that is rank 30. Then, when you enter a mission, you will sometimes see a yellow orb pop up somewhere on the map. Collect this yellow orb. For the next 45 seconds, a percentage of affinity earned by a piece of gear with a lens on it will be converted into focus points for that school.
At your operator, you should see the 5 schools, and how many points you have in each. Upon selecting a school, you can click on nodes to allocate focus points to them and unlock them for use. You can also click on unlocked nodes to toggle them on and off. You can only have a certain amount active at a time, but you can increase this cap (known as the "pool") with focus points.
1Make sure you buy the correct type of lens for the school you wish to level! Though if you get the wrong one, fear not! Leveling all 5 schools is possible, and some would say, recommended.
2It is also important to note that once you put a lens on a piece of gear, this lens cannot be removed. It can be replaced, but the original lens is destroyed in the process.
3Also, there are upgraded forms of lenses that you can craft: you can turn focus lenses into greater focus lenses (blueprint available from the market), and you can turn those into Eidolon focus lenses (blueprint available as a rare drop from bounties).
