A lot depends on the design.
However, with the right design all you would need is a milling machine with a boring bar, milling head, some drills, taps and dies.
If you added a swear box you would soon have enough money to buy a lathe which would help considerably even if you only have a single tool for it.
If the model is small enough/lathe big enough, you may get away with only a lathe but I recon a milling machine is used more.
On the learning side, there are 2 parts from what I can see. The 1st part is the skill of controlling your hands in the correct manner, being able to turn the machine handles smoothly and knowing by the feel/sound/smell how much metal to take off and when its not right.
The 2nd part, which some people simply don't have the ability to do, is to think of what you are building as a 3D cad drawing in your head, and see how you will machine it, which parts need machining in what order so you don't remove the job and then have to put it back again (because once you move it, you will never get it square again).
The 2nd part I would say is the real skill. You could also say to know how to machine you need to know the machine, how it works, how it is meant to work, why it doesn't work the way it should and, most importantly, how you can make it work the way it shouldn't.
A lot of people start off with a simple model, like Stuart Turner.
This is the model type I 1st made:
http://www.stuartmodels.com/inprod_det. ... /mod_id/40
It took me 4 weeks over Christmas one year.
This is the list of tools, machines and consumables I used to make it with:
Big Lathe
Small Lathe
Milling Machine
3 jaw chuck in big lathe
3-jaw chuck in little lathe (the big one was too big)
4-jaw chuck from little lathe held in the big lathe 3 jaw chuck (big lathe is easier to use)
Rotary table
Various sized reamers
Boring bar (used on big lathe) - alternatively I could use one on the milling machine, or on my newly-acquired horizontal boring machine.
20mm carbine milling cutter
10mm (or somewhere around that) domed head milling cutter
Large selection of drills
Tilting table on small pillar drill
1/8" milling cutter
Standard centre drill
1/8" centre drill
Counter sink
Deburing tool
Precision vice - on the milling machine
Set of parallels
Taps
Dies
Tap and die holders
Tapping drills
Cutting Oil
Face plate for big lathe
Parting tool on big lathe
Lathe centre
Drill-chuck centre
Assortment of small files
Blow torch
Bench vice
Solder
Soldering flux
Mini G clamps
Hacksaw
Carbide lathe tool
Small rounded HSS lathe tool
Small pointy HSS lathe tool
Buffing wheel (for polishing the brass)
Loctite