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(There's an exception for legally emancipated minors.)
So, technically, you have to enter into any agreements on behalf of your son.
Practically, I don't think there is generally any checking on this. Some registrars and hosts may ask about age, but I don't think it's commonly asked.
Generally, you have a credit card, (or perhaps PayPal account) you're good to go. Of course, a minor cannot have a credit card without a parent having signed for it. (Though I'm sure - given that they've been issued to cats, dogs, and goldfish, that more than a few slip through.)
An interesting side issue I've never really thought about - what, then, is the legal status of shrink-wrap licenses, EULAs, site terms and conditions, etc. with regard to minors?
I am not aware of any legal age restriction on domain ownership although your hosting service is perfectly entitled to make restrictions of its own.
There are some exceptions - entertainment contracts, for example.
It is apparently NOT the case (as I had assumed) that such contracts are automatically void - but only if the minor decides at some point to void the contract.