Just going off the NPR episodes (which I posted a link to up thread) Ben must of have had some kit laying about. At the least stuff to upkeep his and Anakin's sabers. Plus stuff that he had intended to give to Luke when he was old enough. So maybe Luke just kitbashed one together from spare parts.Yeah I'm pretty sure Luke didn't know how to build his own lightsaber unless Yoda told him offscreen. I've always liked to think that Luke used his own technical skills (much like Anakin) and was guided by the Force to build it. I do wonder what he used to power it though.
Maybe Obi-Wan kept some spare crystals around. That, and according to KOTOR, they could use Krayt Dragon pearls or whatever from the native Krayt dragons of Tattoonie. Hence the big skeleton in the beginning of ANH. But really, who knows.
And do we know what happened to Qui-Gon's saber? Maybe Obi-Wan had it and Luke pulled the crystal out of it.