There are plenty of guides out there for the quick and painful ways to get a legendary weapon. This guide is certainly not one of them. This is a guide for people who get bored if they do the same thing for more time than it takes to boil the kettle, this is the guide for people who don't like tagging along on the zerg-train as the crowd cycles through the same four events to gain karma, or doing the same dungeon path a billion times in a row. This the lazy-toon's guide to loafing to a Legendary.
This is more of a preliminary post - so I'm titling it "The Prep". This is the lazy guide, true, but we aren't going to make it more difficult for ourselves by being unprepared, so these are the things you'll need to know before you set out:
First off, learn the process - you need well over 2500 items in total to get a legendary, crafting mats, mystic forge items, gifts and other gubbins, keeping on top of it all is kinda tough, so make sure you don't get swamped. It might be worth making a spreadsheet or just a list you can mark off when you hit a target.
Some of the tasks you'll have to do are inherently plus-wealth (you can only GAIN money by doing them, there is no way to buy them) examples being the Gift of Exploration, the gathering of karma, badges of honour and doing your dungeon runs. There are also inherently minus-wealth tasks (you can only SPEND money doing it, there is no way to earn it) - examples being your 100 icy lodestones, and buying the recipes for your crafted gifts. Then there are those hybrid tasks which tread the line between: things like the precursor, where you have to make a choice between time (or randomness) vs money. If you don't want to spend ages farming for it, then it will cost you a bagload of money, but if you don't have the money to pay for it, then it's going to take you a long time farming. Other examples of hybrid events are getting your rare lodestones and crafting materials.
The ultimate point is: I would suggest starting your plus-wealth tasks and any hybrid tasks where you choose the timely/random option first, that way you should earn some of the money for the minus-wealth and costly hybrid tasks later down the line. So, by the time you've completed 100% exploration, gathered 500 badges of honour and gathered 1m karma - you'll probably have enough to buy some of your crafting materials and lodestones.
Leave the things which are never going to change in price till the very end - because you're never going to get sucker punched by the market. Icy lodestones are always (presumably) going to cost 1g each, but Charged lodestones might fluctuate in price (particularly atm with the new update!) so you might want to pick a few up whilst they're cheap, and farm for them when they're expensive (and perhaps tactically sell any you get as drops to buy back later at a lower price). Picking up your icy lodestones early might take vital funds away from picking up a bargain in the trading post somewhere down the line.
Gather as you go along. If you always make sure to pick up all your crafting materials whilst farming your karma, exploration and badges then you should have a nice stockpile to train your two lvl400 crafting professions, and a good start on gathering 250 of each of the T6 crafting materials you'll need for your gifts of Might and Magic. Plus it's decent experience to put towards your skill points (which are more of a limiting factor than you think, believe me!).
Salvage all level 75+ rares with a decent salvage kit in order to get Globs of Ectoplasm. Ectos have been steadily rising in price over the past few months, and though they might drop a little with this new update you're still going to need close to 500 for the whole process. So even if the rare you have found might sell on the TP for 30 silver, it is always worth salvaging it down with a mystic or superior salvage kit for a chance of netting 3 globs, a high level crafting material and whatever rare rune is on it.
Finally, my biggest tip is go at your own pace. If you find you're doing the same frustrating task for hours and it's driving you bonkers, then switch and do something else for a while. Most tasks feed into each other in some way (ie, you'll get karma, gold and experience whilst exploring. You'll get T6 crafting materials whilst dropping stuff into the Mystic Forge for clovers. You'll get rare drops to salvage for ectos whilst doing dungeons for tokens etc) so pretty much anything you do will contribute in some way to your getting your legendary.