Well, it depends how "home-made" you wanna make it. If I were to do it, I'd just buy a genero-frame (as they are available) a little 2-stroke motor (at least 2 HP, up to 10 or so.) and then, I dunno, figure out the rest.
Sort of a random suggestion though: when I was in elementary school, my friend had a home-made go kart (with the works...it used a 1 gallon milk jug as its gas tank

) and instead of having a gas PEDAL and a brake PEDAL, he took two brake levers from a bicycle and mounted them on the back of the steering wheel...one for your right hand and one for your left, so he had a brake lever and a gas lever, and it was really really cool to drive that way...pedals are just sorta boring but the behind-the-steering-wheel pedals made it feel like an F1 car's paddle shifts. Very cool sensation.