Leveling alts.

[Kalise]

Duties, duties and more duties.

Be they Roulettes, dungeon runs (The highest level dungeon you can queue for will give more exp than doing a non-daily bonus Roulette) or Deep Dungeons (PotD/HoH).

Throw in a dash of Beast Tribe quests and Challenge Log completions here and there and that's the leveling experience for non-primary jobs.

As a sidenote, if you're finding queue times to be a bit long (Either because you're playing at off-peak hours and/or are a DPS) for duties, up to level 60 you can run dungeons with Squadrons from your Grand Company if you have a high enough rank to access them. Get yourself a couple of Archer and a Marauder squaddies as they do the most DPS and you're good to go with any set up (There's only one healer class for squadrons which you're given straight away).

That said, there is a gap around level level 32-41 where only Brayflox's Longbox is available (No Cutter's Cry or Sunken Temple of Qarn) which can get repetitive... Trust me, I leveled 12 jobs up to 60 via Squadrons and so did Brayflox around 200 or so times due to that >.>

Also, bear in mind that with Squadrons, the exp comes from killing stuff rather than completion, so you'll want to run around killing everything rather than normal dungeon procedure of rushing right to the bosses (Though, it does mean you get full benefit from exp boosts, such as the ring from Halls of the Novice, food buffs, FC buffs, Stormblood/Shadowbringers pre-order earrings etc)

[Nicodemus_Mercy]

So...a silly question perhaps, but how does one level alts if we've already done the MSQ? Just go around and look for quests that were skipped or duty the whole way?

When leveling my main job I purposefully skip all sidequests that don't unlock something and focus exclusively on the MSQ. All those skipped side quests I do on alt jobs for shots of xp here and there.
The primary sources of XP for my alt jobs though are:

Squadron Dungeons, Challenge Log, and daily Leveling Roulette (healers only) 1-60
Daily Main Scenario Roulette, Challenge Log, Beast Tribe Dailies and daily Leveling Roulette (healers only) 60-71
Trust Dungeons, Challenge Log, Beast Tribe Dailies and daily Leveling Roulette (healers only) 71-80

I don't like tanking group content so I stuck to mostly Beast Tribe Dailies and Challenge Log stuff for those jobs.
I am pretty terrible at most of the DPS jobs, am not a fan of melee in general, and don't want to wait for long queues, so Squadrons and Trusts are amazing for leveling the DPS jobs. I do hit the Main Scenario Roulette on DPS jobs for 60-71 though since that's a dead zone for Squadrons and Trusts.
I love to heal (I main WHM), and am more than happy to run leveling roulettes on any healing job.

I hit fates from time to time when convenient but I don't care for fate farming. I still don't have the ShB shared fate stuff completely unlocked. 60 fates per zone is just too much to ask of me. I think I've done maybe 10-15 fates in each zone so far.
Deep Dungeons are fun in small doses but I can't chain run them too much cause it gets too repetitive and monotonous for me.

[ADarklore]

Also, don't forget your Weekly Challenge Log. It can be a little annoying at times to have it work out but try to at least do the "final step" of each Challenge on the job you're trying to level. You can even do the FATE and Levequest weeklys in a low level zone to blow through them very quickly (and the FATEs will help your chocobo companion level too if you don't have it capped yet).

^THIS! I do the weekly FATE and LEVE Challenge log in low level zones as they go very quickly and offer very high XP rewards.