When FFXIV: A Realm Reborn first launched, leveling was rather simple, you joined a big FATE group and you moved FATE to FATE. There is a lot of interesting nuances to FFXIV leveling, because you need / want to level to 50 on various jobs on the same character, but some content is one time only. Interestingly enough, once you reach 50 on one job, all the other jobs receive a 50% XP boost, making it easier to level through FATES, dungeons, guildleves, levequests, etc. Post 3.0, main scenario (or story quests) give additional XP to help with the grind to 50, but that ends at any quest that is level 50 or above.

This guide is mainly intended for 1-50, but 51-60 follows the same formula. You'll naturally have the same method of leveling, but you'll have quests again and once you consume then, you'll have to rely on guildleves and FATEs once more.

Things to Make Leveling Easier 

Always do the daily roulette for the first of the day bonus. This can sometimes net nearly a level of XP, if not just enough to ding anyway. Do the dungeon and the guildhest. If you're DPS, queue and do other things, while tanks and healers can expect near instant queues. This has to be done solo, so it's best to do it before your friends want to play. 

You can get an EXP buff from food. The cheapest food is fine. 

Always log out in a sanctuary, it's just smart to build up that rested EXP. 

No matter what, grinding is usually a bad option, unless it's something specific like grinding mobs in a fate that spawns a ton of low health same XP monsters. 

The hunting & challenge log will grant you EXP for simple tasks, like killing x number of enemies (hunting log) or completing 5 dungeons (challenge log). The challenge log resets each week and each assignment in the challenge log gives a % of your current EXP level. You get the challenge log through a sidequest at 15.

Leveling the Easy Way on Your First Character 

The easy wasn't isn't the fastest way, but here's what you do. First, queue for a dungeon, dungeons are good EXP even post 2.5, and then quest while completing your hunting log. Quests are probably the easiest most mindless path of EXP and there is no point in saving them, honestly, with the 50% boost to your secondary jobs, leveling changes a lot, such as the ability to spam guildleves and it be worthwhile, whereas on your first character guildleves, even the "exploitable" ones, aren't that great considering you can't do them 5 levels early and you aren't getting 50% more EXP.  

Let me back up, on your first character your best bet is to follow the main story. The main story is going to be the vast majority of your experience and lead you to where the quests are. Quests, main story, and dungeons, are plenty of enough to get you quickly from level 1 to 50.  

FATES are useful for your challenge and hunting log (hunting if something spawns in the FATE), but otherwise can be ignored unless you need some EXP to cover a gap between storry scenarios. Considering the double story scenario EXP and the fact you must complete the story to explore Heavensward, there is little to no reason to just not level up your first character on your story missions. Dungeons are great, daily quests are good, but ultimately the main story and side quests, along with dungeons and guildhests are going to get you there the quickest. 

Heavensward's launch makes the main story quests grant additional XP, to help you get to level 50 faster (which helps you get through 2.55 content to reach Heavensward content and the grind from 50 to 60). 

After 30, you might run out of things to do quest wise at some points, but post-3.0 that's a rareity, unless you've done all the quests already. 

Don't forget your job quests too! They unlock additional EXP.

Leveling the Efficient Way 

To level quickly after level 50, you'll no longer have the main quest and a plethora of side quests to drag you along, and FATE leveling is considerably slow (although not useless). You have 50% extra EXP on your side, plus whatever rested you've gained, plus food, so everything is much easier. 

The "easy" option is to repeat the above advice, do the quests you can while grinding dungeons. However, that's not specifically that great of advice. Guildleves on the other hand, oh ho ho, that's where the money is at. 

A level 35 guildleve turned to the maximum level gives 10,000 EXP, but add in doing it five levels early, plus the 50% EXP bonus, and you're at 15,000 EXP per each, at a level where quests give you about 6 to 7k, for something you can grind out rather easily. My math here is probably poor and there is probably some more equations going on, but needless to say a lot of guildleves can be completed without combat, making the additional difficulty a non-issue. 

You earn 6 allowances a day, but can stack 99 of them up, which is probably what you'll have looking at it. They are limited and you will run out. 

So, basically, queue for a dungeon (that's going to be a big boost to your EXP) and grind out guildleves, while you wait for the dungeon. If you're out of allowances, then grind FATES. 

FATEs aren't bad for your second jobs, EXP wise, they're not as good, but there isn't much more you can honestly do if you're out of quests and allowances. One thing to understand is that a combat-less guildleve can be as much EXP as a FATE, if not more. The trade off is that you grind the same thing along, versuses following around a group of players completing FATEs. if there isn't a FATE group running, FATEs are very bad EXP to try and solo.

To sum everything up: eat food, get rested EXP, stay queue'd for a dungeon, do your dailies (especially low level roulette), and grind quests > guildleves >= fates. 

That's about all there is to it! Have fun adventuring, and remember, when Heavensward launches, you get way more EXP from 1 to 50, making this journey even simplier.