HI Ping, I do gunsmithing on the side and have for about the last 20 years, it helps feed my habit.
I started because I could not afford to pay smiths to modify my guns, and truth be told, many of them did not want to do what I wanted or thought I needed. I have a mechanical background to begin with and good complex motor skills, used to have great eyesight, now in the shop I use a magnifying visor. Now to your question.
1) Gunsmithing is a huge term, in the beginning, a true gunsmith, could build a gun from raw materials, so blacksmith skills, metallurgy skills, metal shaping, threading, filing etc... some countries still have this requirement, to be called a Gunsmith.
2) This is probably not what your after, so define, what you want your capabilities to be, Pistolsmith, Riflesmith, Shotgunsmith?
3) Within these categories, is a lot of room, Repair specialist, Modifier, Maintenance specialist, Diagnostician, Accuracy specialist, metal refinisher and what most of us are, general gunsmith, you can do all of the above, but don't have machine tools for turning barrel blanks, and threading equipment, Don't have milling equipment, or bluing equipment, metal treating equipment etc... or just basic types, for touch up.
4) Pick what you want to be, I started off as a modifier, mostly action jobs and trigger jobs, then customers wanted new sights that needed machining, So I bought a milling machine.
5) Then they wanted, rebarreling, got the jigs and learned the know how on 1911's, revolvers you just screw on, but there are rules to follow, so as not to bend the frame, and if the barrel does not index properly, rules for correcting it. Some easy, others not.
6) Now subcatagories, do you want to be a manufacturer specific or model specific smith? Remington, Winchester, FN, Browning etc.. Or AR15, 1911, S&W revolver, and to the subsections of these, 870 mechanic, 1100 smith, 1187 smith, 700 smith, A5 smith, J,k,l,n,x frame smith, Colt p frame or d frame? Single action revolver, and lever action very popular these days.
7) Confused so far? Start at the beginning and develope a niche that you are really good at and then exploit it, most of us, start off like me, Maintenance is a good place to start, take inventory of your personal firearms and learn them intimately, learn polishing techniques. There are many good DVD's from the American Gunsmithing Institute, not bad for repair, but forget much good modification technique, they are too scared of getting sued, but good info, there are lots of good books, Kuhnhausens stuff is good, Colonel George Nonte, Home gunsmithing is a must, as it go's into spring making and rebarreling, and from a time before lawsuits, and when smiths had to make things or bend things to make them work. For S&W revolvers, Jerry Miculeks dvd, although poorly filmed is right on, Hallocks book on the .45, 1911, is a cheap must have book to start.

Watch the how to's on Brownells website, good info for free.
9) One of these days I will take a working vacation and take Bill Laughridges, Cylinder and Slide shop class on 1911's, the best as far as I have seen.
10) You will have to invest in equipment, at 1st, good files, stones and screwdrivers with hollow ground bits, fine shotguns, like double barrels, SS and OU, you might have to grind your own bits to fit. Some good punches, including roll pin punches, then as you progress, barrel jigs, sear jigs, bench blocks, bead blaster, large quantities of solvent, degreaser, lubricants of all kinds, rust remover, fine and course abrasives, polishing wheels, and a motorized bit holder and electric motor to mount them on, belt and disc sander,the list go's on.
It is a satisfying profession and you learn something new everyday, A customer brought me a Remington Model 81 today, never had one apart, but nows the time. He can't load the magazine, .300 Remington, that has been rechambered, at least that is what is on the bolt, to .300 Savage, We will see.
