So you want to build the Enterprise. Don't we all! Well good news: according to some quick, messy, napkin math, it's possible. Kind of. The bad news? It's going to be stupid expensive. But not unfathomably so! Start scrounging up your space-pennies.
One little constraint
Since we can't predict the future, or even come close to gauging the cost of development for revolutionary new inventions or substances like warp and impulse drives, shields, and teleporters, we're going to stick to what we know. It might not make us a real Enterprise, but it's about as close as you're going to get.
So where do we start?
First we have to pick our Enterprise. Obviously, with Star Trek: Into Darkness coming out, we're going to go with the one from that universe, from a size perspective anyway. According to some stats we got back when the original Star Trek reboot came out a few years ago, we know the new Enterprise—or as the Star Trek wiki calls it: USS Enterprise (Alternate Reality)—is 725.35 meters, 2379.76 feet, or roughly half a mile long. So, huge. And while the exact measurements vary, other sources give us a height of 625 feet, and a saucer diameter of 1,000 feet. She's a big girl.