Any silver account can be upgraded to a free 30-day gold trial account with a valid credit card. You have to put in your credit card information, and after 30 days you will be charged $8.99 a month if you do not cancel. If you hit the Xbox button while the Xbox is on and your son is signed in to his account, one of the options should be something along the lines of "upgrade to gold account." Select this, and then follow the process. It will ask you for account information/credit card info. See for more details: http://support.microsoft.com/kb/908657
If he (and you) decides to keep using a gold account, it is much cheaper to cancel the subscription, and buy a 3-month or 12-month prepaid card. They also sell 1-month cards, but from what I've seen they're actually more expensive than a 1-month digital subscription ($9.99), so not really worth it. You also don't have to worry about automatic re-subscription if you use these prepaid cards. If you're buying a years worth, it can be a issue to have your credit card automatically hit for another entire year of gold because you forgot to unsubscribe. To redeem these prepaid cards, hit the Xbox button, go one tab to the left, and select redeem code. You can typically buy these cards at any department/electronics/game store. Keep a lookout online as the $60 12-month cards frequently go on sale from $35-$40 with free shipping. Typically Amazon runs deals like this, but a quick query on your search engine of choice should find you the best deal. The only downside being you have to wait for the card to ship if you purchase online instead of in store. You can also purchase a digital code to redeem instantly online(Amazon definitely does this), but these are usually still $60.