How do I dial in Japan using an iphone?

My son has an iPhone which we want to use in Japan, both to phone our Japanese friends and for them to contact us. I have my friend's mobile number, which I assume I can just dial straight but if she wants to contact us, will she have to dial a prefix number before the actual mobile number, because it is British-registered?

I'm not sure but seems that'd have to go both ways.

I have my friend's mobile number, which I assume I can just dial straight

Dial as if your phone is in the UK, so calling Japanese numbers would require you to include the international prefix (+81) for Japan.

but if she wants to contact us, will she have to dial a prefix number before the actual mobile number, because it is British-registered?

Yes, she will need to also use international prefixes because she is calling a British phone number.

and it will cost a fortune in roaming fees, consider getting a prepaid sim at narita airport.

Yeah, be sure you'll be able to actually use your iphone with a japanese sim card beforehand (I mean, that your iphone is unlocked), and then buy a pre-paid sim at Narita or once you get in Tokyo. Otherwise your following phone bill will be astronomical

Surely if my son turns his data roaming off and just uses his iPhone for making and receiving calls, he will only pay for the calls, which shouldn't be too expensive.

It depends on his plan but be prepared to pay several hundred yen per minute for international roaming. If you make more than 1-2 short calls per day then then it might be cheaper than getting a rental or prepaid sim.

I once made an 8 minute call to Detroit from Tokyo and it cost me $26.50

Surely if my son turns his data roaming off and just uses his iPhone for making and receiving calls, he will only pay for the calls, which shouldn't be too expensive.

Check with you local telco the cost of making and receiving calls while overseas: International Roaming Rates on Mobile calls are astronomical: be careful, be very careful.
Turning off data roaming will only affect Internet charges: on an iphone, be sure to turn off BOTH Data roaming AND Cellular Data (so Push Notifications dont get charged)
AND expecting local Japanese friends to essentially make overseas calls to you might be a little unfair.