Step 1: Overview
Well, as the immortal John Belushi said: (loud belch) ... "why not!?"
Our Good Book is the Orange Book of St. Gingery - also known as "The Metal Lathe", by the late Dave Gingery. This handy pamphlet-ish book, the 2nd of a series of 7, has step-by-step instructions for folks wanting to build a lathe from scratch. Many folks around the world have built or are building "the Gingery lathe" -- there's an entire newsgroup on Yahoo dedicated to 'Gingery machines', as well as a ton of websites.
I'm putting together pictures, notes, and so on, to help others on this sacred journey -- and for a few friends who think I'm nuts (but secretly wish they could do this if only their wives would let them, and if they thought they could get away with it without burning their ... ummm ... fingers ... off).
The books are available at Lindsay Books' website, and/or at Amazon, Barnes & Noble.com, etc. Check out: http://www.lindsaybks.com/dgjp/djgbk/series/index.html for the main series.
This is how the project works: (a) You make 'patterns' of the parts, out of easy-to-work stuff like wood (pine is good), plywood, hardboard (the dark brown stuff that lots of pegboard and 1950s elementary-school fixtures are made of), etc. (b) You make molds in sand, with a few other ingredients; melt metal (easier than it seems, and DARN good fun!); and pour the molten metal into the mold cavity. And, (c) you combine the parts you make, with a few bits of steel, machine bolts, and such, from the local home center or hardware store.
Tools needed are simple: while a drill press is VERY helpful, the plans are designed around simple tools like a power hand drill, a few threading taps (not too hard to borrow, or fairly inexpensive at the local home center/hardware shop), etc.
The most important thing, imho: you'll learn a LOT about Making Things -- metal casting, machine tools, parts, tolerances, etc. -- it's a thrilling learning process! And - when you're done - you'll have the core component of a fully functional machine shop!