Spot on with the transport card. He should get a Suica card (or Pasmo) from one of the ticket vending machines (of which there are plenty at Haneda airport). I'd suggest putting 2000 yen in the machine and they will get him the Suica card with 1500yen of opening credit. He can top up as needed.
Importantly, this works for ALL public transport in Tokyo - there are multiple systems run by different companies, but the card is universal.
From the airport catch the Monorail into town. This arrives in Hamamatsucho where you can connect to the famous Yamanote line which is the main ring route around Tokyo.
As for what to do, I'd strongly suggest seeing the TeamLab Borderless exhibition, which is getting rave reviews at the moment. We went last month and it was outstanding. Get there are 10am with a prepaid web ticket.
teamLab Borderless Tokyo Official Site :MORI Building DIGITAL ART MUSEUM
Shibuya is also a good option, a quintessential tokyo experience, and it's on the Yamanote. Maybe head there for a late lunch.
Google maps is probably the simplest option for working out the train connections around town.