Click on the Schedule button and you will see the screen on the right. At the top left corner of the screen, you can see how many tickets you have to advance the Schedule and at the right you can see a list of Schools and their respective rank. The number of tickets given per day can be increased when the Schools reach certain combined ranks. +1 ticket per day is given at the combined ranks of 10, 25, and 50. This means that you can reach a maximum of 6 tickets per day. An extra ticket can also be bought in the daily shop for 30 pyroxene.
After clicking on a school, you will see a screen with icons of students and a bar at the top right. Selecting an icon from the ones shown will consume a ticket, increase affection with the shown students, and possibly give other rewards shown beforehand like books or shards of that student. The rank bar at the top right will also increase by 100 with every schedule you select in that particular school. New areas can be unlocked as you rank up.