90 Day Temporary Visitor Status

Hi, I'm from a country that does not require a visa when entering as a tourist for 90 days or less.

My question is how is the 90 days defined? I'm asking this because I'm planning a 3 month trip in Japan and want to stay for the full length of the visa.

Example, my flight leaves on Jun 25, arrives in Japan on Jun 26, is the day I arrive in Japan count as the first day? So if I schedule my return flight for Sept 24 Japan time(i.e. the 90th day AFTER I arrived in Japan but the 91st calendar day that I'm in Japan), have I overstayed?

Your 90 days start the second the Airport immigration staff staple the temporary permit in your passport. So if you land at 10 pm in the evening that 1st day is gone. It ends on the day of departure so that day may be wasted by going to the airport and waiting etc.
better be safe and leave japan on the 89th day..
so your actual sight seeing trip would last 87 days..hope that you have a sizable budget...