To take it straight forward, this is not a comprehensive guide. Even though I'm going to go over the standard fare and then go over one of the hard truths of the game about how gil is obtained. The following may help you a little:
The Basic Ways to Farm Gil
You can farm gil from a plethora of sources, each of them give you a variety of income. Dungeons, quests, the challenge log, and allegan pieces from quest rewards are all very viable means of farming gil. The main story scenario should land you easily with 300,000 gil or more at level 50 and even more additional gil beyond even there.
Going to dungeons that are now far below your level (at level 60) and cashing in on the treasure chests is another viable way of earning coin, along with just outright nearly soloing a lot of the content. Slightly controversial, but selling a "carry run" through the early level content and especially some of the harder to queue for dungeons is an attractive means for players to make gil right now, although that tapers off in a month or two after posting this guide.
Anything you do in the game will earn you gil, but most of the activities are not very profitable to just grind at. For that, you'll need to sell items to other players.
Crafting, Gathering, and Even Being a Disciples of the Hand and Land
In FFXIV, the best way to acquire gil is through either gathering, which is profitable even at level 1 for shards, crafting which players very much need crafted gear, or through otherwise acquiring loot to sell on the market. While you can grind enemies and quests for a bit, you can just as well find a non-bound item and sell it for 10 to 20k Gil easily no matter its level.
The items you get out of dungeons sell really well, along with any crafted gear for the new Heavensward job classes. Even as players settle in on post 3.0 content, it's most likely going to remain a crafter world in the gil farming circuit.
Don't fret though if you haven't maxed a crafter out yet, gathering simple low level ingredients and selling them is necessary for other players to level up their crafters.
At any given point in FFXIV there are trends in items needed for the new content. Leveraging gathering and/or crafting to gather and / or create these items will always be one of the best sources of income.
Finally, the staple of everything, converting. Spiritbind gear to yourself to 100% then convert it for the materia, then sell the materia on the market. Looking at materia prices on my server, Coeurl, for IV series is around 5,000 gil. 3k to 10k is reasonable for the various types. If you get a V series, you're looking at millions of gil right now, and surely some rather high prices throughout the game. I'm seeing almost none available and the few that are around 7 to 10 million.
Savage Might IV is at 15,000 as well. Spiritbonding and desynthing is definitely the way to go. Crafters can craft a full set of gear to spiritbind, then sell the associated gear.