Well....

All things considered I'd say get another bike. If he want gears, then he's probably looking at more utility-oriented riding, and you can't beat having fenders on a utility bike.
On top of that a lot of people find drop bars an aquired taste. If he hasn't ridden enough to find room in his life for owning a bike he isn't going to have much use for drop bars.

But if you insist:

Assuming the rear dropouts can be spread, the cheapest way to is to get an new rear wheel. You can probably get a cheap one with a screw-on freewheel off a hybrid. Next a Shimano low-end derailer with integrated hanger. It'll bolt right on. Then you need a thumbshifter that can do friction, which you put on the flat portion of the bar up by the stem. A few feet of cable housing, a cable, some zip ties and you're done.
Keep in mind that many people would consider this crude beyond belief and an insult to a rather nice frame.

The "I-dare-to-ride-this-in-public-during-daylight" approach is to get an internally geared hub instead. You might want to look at which ones there are drop bar adapters for first. JTEK and HUBBUB are two source that might be worth a visit. Then go crazy googling for "cable stop". There are a couple of places where you can buy nice wraparound ones, saving you the indignity of having to run housing and zip ties all over the bike.
You'd be able to pick up a perfectly nice beater bike for considerably less money than what the IGH alone will cost you.