We are traveling from Tokyo Haneda to Osaka

How easy is it to buy tickets in advance?
I have used the 14 day JR rail pass calculator and discovered that it would not be worth buying as we will not be moving about enough during our stay.
Thank you,
Martin
UK

In person: you show up at a counter, tell them the date/time, pay, and they give you the tickets, with your assigned seat printed (if you booked a reserved seat).

Online: https://global.jr-central.co.jp/en/tickets/buy/
Disclaimer: I haven't used it myself. I tried to book on the JR West website once, and my foreign cards (Visa and Mastercard) kept being rejected.

Are you sure you want to buy your tickets in advance, though? The trains from Shinagawa to Osaka run very frequently, every 10 minutes or so. Also, your flight might be delayed, so it might be less stressful to just buy a ticket a the train station.

Agree with Mellye.
It's better to buy the shinkansen ticket at the station since you might need to adjust due to your arrival time + time you come out of the airport. I tried purchasing the ticket both from a machine & ticket counter, pretty straightforward for both.