Note: Most Loppi pages are unfortunately in Japanese. Although you can switch some of the main text to English, to purchase Studio Ghibli Museum tickets, it helps immensely to be able to read Japanese.
On the Loppi home screen, there’s a button for Mitaka Ghibli Museum. When you click this, two options appear for which month you want to purchase a ticket. When you select the month (look for the month number next to the symbol 月) a calendar appears where you can select the day you want to visit.
Select the time (10:00, 12:00, 14:00, or 16:00) then select how many tickets of each type you want to buy. Adults cost 1000 yen, ages 13-18 are 700 yen, 7-12 are 400 yen, and 4-6 are 100 yen.
Tip: Studio Ghibli Tickets are purchased under one name, so only buy tickets for those you are going together to the museum with! If you are purchasing for another friend or group that is going on a different day/at a different time, you have to make a second purchase under a different name.