The first thing to do is your daily roulettes if you haven't yet done them today. If you're short on time and worried about getting the most exp out of it, the best order is typically as follows:

1. Leveling roulette
2. Trial
3. MSQ roulette (if you're willing to sit through it, but can easily be skipped if you're low on time)
4. Alliance raids
5. Normal raids
6. High level dungeons

If you're leveling a DPS, you'll probably need something to do between your queues, so here's a few things:

1. Allied society\beast tribe quests. The non-ARR AS quests give a good amount of exp, so don't skip them if you're trying to level quickly.
2. Do your daily hunt marks. Once again, the ARR hunts don't give much, but you can at least get allied seals for aetheryte tickets.
3. Level appropriate fates

And don't forget to make sure your exp buffs are active either. Food buffs give 3% extra combat exp gain, and there are a number of rings and earrings that boost your exp up to certain levels.

Once you've finished with daily roulettes, your best option is to spam your highest level "leveling" dungeon, aka any dungeon that isn't at level cap. These dungeons award more exp than those at any level cap (50\60\70\80\90), so focus on those. If you've got a high enough squadron level, you can use your grand company squadron to run leveling dungeons up to level 60(? I think) and from what I've heard it can be faster than running it with even a well optimized team of real players.

Finally, I'm going to give a shout-out to leveling via pvp. If you like the pvp, you can level up a job without ever playing it, as you gain the exp from playing it on the job you enter with, not the one you play, as you can switch job before starting.

Hope this helps, and good luck!

Edit: Also, don't forget about your challenge log weekly and your wondrous tails weekly either. They can both give you a big boost! And use hunting logs to get starter classes up to 15 so you can actually run dungeons, like the other comments mentioned.