Japan begins its vaccination of 36 million over-65s against Covid today. A short
with some things to keep in mind...

Japan has vaccinated more than 1 million medical workers (nearly half with both doses). For the next 3-4 weeks you'll see lots of takes here along the lines of "Japan has still only vaccinated x% of its population, at this rate it will take until <year very far away> to finish!"
Ignore these; don't expect an immediate ramp-up in numbers. The rollout won't begin in earnest until after Golden Week (May), when large amounts of Pfizer start to make their way to Japan. This schedule is public info but you can expect the "behind schedule" takes regardless
Japan aims to distribute both doses for all >65 by end- June. They're on track with Pfizer alone, with 43m doses to arrive in May and 45m more in June. This does NOT mean that all of those over 65 will be vaccinated by end-June - expect that to take longer https://www3.nhk.or.jp/nhkworld/en/news/20210409_22/
With 97% of all Covid deaths in Japan in >60s they have obviously been prioritized first. What about the rest of the population? That's a little less clear. Those with underlying medical conditions and 60-64s are next in line. Officials have been vague on what happens next.
One reason for this may be that in May, Japan is expected to make a decision on approving Moderna and/or AstraZeneca. With officials already planning to use Pfizer for >65s this will open a new source and should(?) hopefully lead to more clarity.
For now, Japan's giving an initial shipment to every municipality in the country. Municipalities are doing things differently e.g. Hachioji took bookings for today; Setagaya is using its allotment for those in nursing homes. Expect road bumps! https://news.tv-asahi.co.jp/news_society/articles/000212684.html
Keep in mind: like other countries such as S.Korea that contained but didn't eliminate Covid, Japan doesn't need vaccines to "reopen society" - schools are open, most still work at the office. Gyms, cinemas barely skipped a beat. Bars/restaurants close early, but are open all day
(For perspective, the UK today will open pubs *today* for the first time since *December* only after vaccinating 32 million people. There literally hasn't been one time during the pandemic when you couldn't get a meal and drink in a restaurant outside in Japan)
Nonetheless, the vaccine rollout is going to be essential to long-term control of this thing -- but the biggest challenge is going to be convincing a vaccine skeptical young public who are largely in little danger of even GETTING Covid that this is something they need to do.