There seems to be some confusion as to what exactly constitutes being a "gun collector", so let's start by defining it by what it isn't:
"Fred, who lives next door, has a pretty nice little gun collection. He has his dad's service pistol, that shotgun to shoot sporting clays, and that little pocket Beretta." Fred just happens to own guns; he doesn't collect them.
"Joe from work is a hella big gun collector. He's always horse-trading, has to have one of whatever was on the cover of Guns & Ammo this month, and can't pass up a gun if it's on sale." Joe is not collecting; Joe is accumulating.
"My uncle Frank has quite the gun collection. He's got a beautiful Weatherby he takes after elk with every year, then there's all those bird-hunting shotguns: one each for duck, pheasant, and turkey. Oh, plus all those guns he uses for Cowboy Action Shooting." Your uncle isn't a gun collector; he's a gun user.
"I hear tell old man Rogers down the block is a little touched in the head. He's got, like, one of each Japanese military rifle ever made, and some of those old things cost him thousands of dollars. And get this: it's not just one of each rifle, 'cause he's got one from each factory that made 'em, and then like one from each year from each of those factories. To top it off, he's only got maybe a hunnert rounds of ammunition, total, for all those guns, 'cause the ammo's so hard to find, and costs like two dollars a shot." Old man Rogers is touched in the head: he's a gun collector.
All right, now that you've decided that you, too, want to be touched in the head, how do you go about it? Well, from my experience, I'd offer three pieces of advice: First, define your collection. Second, know your market. Third, make good connections.
Defining your collection is important. "One of everything" is impossible for even the most bottomless checkbook. You could spend yourself broke even if you confine yourself to, say, 19th Century Colt revolvers, Pre-'64 Winchester Model 70s, or pre-war S&W revolvers. Focus is important, and is, in fact, what defines a gun collection. So, decide what really interests you (and what you can afford; a collection of Walker Colts or GE Miniguns is going to put a strain on non-seven-figure incomes) and how much time and money you are willing to invest in the hobby. This is how I picked my two collecting passions: S&W revolvers and milsurp bolt actions. The initial entry costs were gentle, examples are common, they hold my interest, and as time goes on, I can get more serious by focussing down further within those broader fields. Now you're ready start building.
Next is knowing your market. There're only two ways to do this, both of which are necessary: Reading and Legwork. Books like Fjestad's Blue Book of Gun Values and Krause Publishing's Standard Catalogs are only a start; you need to get your hands on the specific reference works for the types of guns you're interested in. Dedicated, specialist reference books are a must, because trying to collect Smith & Wesson revolvers, military Mausers, or Colts without knowing who Supica & Nahas, Ball, or R.L. Wilson are is an isometric exercise: It's strenuous and gets you nowhere. You need to pick up Shotgun News and Gun List, as well as reading through Gunbroker.com and the various internet sites and forums dedicated to your area of interest. For legwork, you need to attend gun shows religiously, and make a habit of stopping in at gun shops in your town on a weekly basis. The net result of all this is a basic, gut-level knowledge of the scarcity and the going market price of firearms in your field of collecting. You should be able to know, faster than your eyes can focus, the rough selling price of the gun you are looking at within the nearest $50 or $100. There are a plethora of factors which can effect the value of guns in various fields, like scarcity, condition, and regional demand, and you should have them committed to memory. Be aware of how badly you want certain guns, versus how rare they are: I once jumped on a 3" 625-7 for a good $100 over what was the going rate for stainless 3" N-frame Smiths in these parts, simply because there were only 200 of these .45 Colt guns made, and I didn't want to wait 'til I stumbled across another one; the market has since vindicated my decision. It's really no different than the effort other people put into analyzing the stock market, except that you can't take a stock certificate to the range and use it to punch holes in the ten ring.
Lastly is building a network. Get to know the small dealers at gun shows who cater to your market. Make friends with them, and you'll be surprised to find how willing they are to bird-dog for you. If there's a collector's society dedicated to your particular addiction, join it, and get to know local members who've been doing this for a while. Benefit from their experience (and the castoffs from their collections.) Get friendly with a local FFL. I have a small stack of cards with phone numbers in my wallet: If I take in a 4" blued S&W K-frame, a Springfield '03, or a pre-war Colt revolver at work, it may not make it to the showcase, because I know exactly who I need to call. If you travel on business, another benefit of knowing a local FFL could be the provision of signed FFL copies. At a shop I used to work at, we had a travelling businessman who'd stop by the shop to pick up a few every time he left town. When he got to his destination, while his fellow conventioneers were out tipping shoe models he'd be off wandering through gun stores and pawn shops and finding nice specimens to send back home, thanks to the FFLs we'd provided.
Being a collector is fun, and doesn't preclude Accumulating (despite collecting milsurps and S&W wheelguns, I still accumulate customized 1911s) or Using (I do plenty of target shooting, and try and keep a varied bag of hunting, plinking, and home defense guns on hand), plus it can add an enjoyable new dimension to the basic human urge to collect stuff: When's the last time a baseball card, comic book, Hummel figurine, or postage stamp went *BANG!*?