(image from Lawson official web site)
Prior to our arrival, I had checked out through Lawson's online system and found there were still tickets available on the day we had planned on going, but then the first night we were in Ikebukuro we were not able to find the Lawson that was supposed to be close to the hotel... I checked on line later and the tickets were gone.
Anyhow, the first morning after we arrived in Tokyo we managed to find another Lawson, and also found there were still tickets for the 4 o'clock admission. We decided to go that day and changed our schedule a bit.
So this is how you purchase the tickets:
First go to the "Loppi" system inside almost every Lawson (the ones in the major cities anyhow).
The top of the Loppi system looks like this. The machine looks like a stand-alone ATM. (image from Lawson official web site.)
After locating Loppi, touch the screen and find the Ghibli Museum button and click it. This was as far as I could go... I couldn't read any more Japanese after this... We asked a lady that worked at the store to help after this.
*It may be a good idea to ask the shop clerk to help as soon as you find Loppi if you can't read Japanese.*
Anyhow, I did know that we needed to have our names in Japanese (Katakana), as well as the Hotel information in Japanese. The lady was kind enough to enter everything in for us when she understood what we needed to do.
These were the key words I used: Miyazaki-san, Ghibli Museum (ghee-bu-li muu-zee-aa-mu), futari (2 people), kipu (tickets). (I also showed her my note that had the date and time we wanted to go.)
The nice lady typed in everything, and then printed a receipt out, told us to take it to the counter and pay for it.
We made our payment and another store clerk printed two tickets out for us.
And yay we got our tickets!
So that day we decided to go to Shimokitazawa, then to Kichijouji, and after that we'd walk to Miyazaki's Ghibli Museum through Inokashira Park.