Getting a legendary weapon is a long, and often tedious process. It involves a ton of grind over hundreds of hours of gameplay, from farming champion bags to endlessly repeating easy dungeon paths to bookmarking Ancient Wood and Orichalcum maps on the Internet so you can sweep through a zone and get the best mats in the least amount of time process. It's a mind-numbing bore that will leave you burned out on Guild Wars 2 and hating life more than a centaur hates humans.
Or will it?
I hate to sound like a self-help infomercial but “It doesn't have to be that way!” I've got one legendary and another on the way – you'll never guess what I need! – and I'm not yet soured on the game. Sure, I play a little bit less than I used to, but I don't have “not that again” syndrome: “Not another CoF run!” “Not more zerging!”
This isn't to criticize any particular style of play. If you can handle, or even like, doing the same thing over and over for hours on end to get loot, hey, more power to you. I'm just challenging the notion that this is the way things have to be if you're looking to pick up a legendary. I'll often see people in chat or on social media saying, “I really hate doing X, but I'll do it because of the loot.”
Maybe you should try, you know, not doing things you hate? It's a pretty good rule to live by in gaming, and in life. And you can get a precursor without hating the process.
The basic premise
This isn't a get-gold-quick scheme. In fact, it's very much the opposite; you'll probably advance a fair deal more slowly than if you were mindlessly grinding to get loot. But that's kind of the point. You have to be willing to trade some efficiency for less damage to your sanity.
In other words, think of this as less instructional and more motivational.
I got my first legendary after about 1,000 hours of gameplay. At ~1,500, I'm just about ready for my second, and have progressed a good ways on my third. Yes, that's a lot of hours. I'm not a noon-til-night kind of player, but I was averaging around 100+ hours a month (according to Raptr) initially. You'll still have to play a lot, but the idea is to avoid repeating the same content over and over in a short period of time. There's no hurry, so spread it out some.
Throughout all that time, I wouldn't say I ever spent much more than two hours at a time “grinding” anything, and sessions of even that length were rare. I farmed skelks in Southsun for Vials of Powerful Blood for about an hour (two or three times), once ran CoF path one three times in a row, have made only two or three continuous circuits of the Frostgorge champion train, only once did two Scarlet invasions in a row... you get the idea. When I get tired of playing, I stop playing. I don't keep going just because I feel I need to in order to acquire loot.
The thing to take away is that a legendary requires so many different things that you're almost guaranteed to trip over what you need just by playing the game in a balanced fashion. Some acquisition methods are more efficient than others, but nearly everything has the chance to get you something you need, from gold to Ectoplasm to skill points to crafting mats. Don't wear yourself out focusing on a specific task; it'll just hurt you in the long run.
Scrooge or splurge?
The best advice I can give you: learn to save. Save like you're feeding your 401(k). You're going to need hundreds of gold, a million karma, and lots of skill points to get a legendary. You'll have to spend some along the way, obviously, but you'll be best served by passing on high-priced luxury purchases, like T3 racial armor or expensive weapon skins. There are plenty of great things you can get for a lot less than top dollar (or gold), and they don't affect your gameplay in the slightest.
At least, that was the case, before ascended items came along. But you know what? I still don't have any. And I don't feel like I need them. A level 80 ascended weapon does 5% more damage than an exotic (which itself does 13% more than a rare). The same ratios exists when comparing ascended armor to exotics. And the materials you require to make both will cost you a ton. A few months ago, I estimated the cost required to make a full set of medium exotic armor at around 60 gold per piece, or 360 gold total. I'd rather craft those bits as I acquire the mats and sell them to other people who absolutely must have the best gear at all times.
Guild Wars 2 isn't the kind of game where you have to have best-in-slot all the time or be a second-hand citizen. I have splurged to get mostly all ascended jewelry on the characters I play the most, since they typically only cost laurels, though you might even try to get by without those, since you can exchange a laurel for a bag of three T6 rare crafting materials.
Basically, take heed of the opportunity cost of anything you plan to spend on, whether you're spending gold, karma, laurels, or whatever. Is what you'll get from it really worth what you'll spend? For me, a 5% increase in damage isn't worth 60 gold (not to mention the cost in karma), no more than a cool-looking T3 outfit is worth the 119 gold it costs. If you get an expensive exotic or skin to drop, consider selling it. Your mileage may vary, of course, but if your goal is a legendary, some sacrifices will have to be made.