How to get to Limsa Lominsa?

[Frizze]

Just continue with the main quest. Not only do you need it for unlocking travel to/from Limsa Lominsa, you also need to follow it to unlock instanced dungeons, as well as loads of other features.
Almost everything in FFXIV is gated behind the MSQ one way or another.

This. 100%. Most of the important things in the game are locked by the MSQ either directly(the MSQ sends you to the other towns so it gives you airship access, it makes you run a dungeon so it unlocks it, etc) or indirectly(for example you wont be offered the quests to unlock some optional dungeons until you finish specific steps of the MSQ). Its always a good idea to be at least reasonably caught up with the MSQ.

Side notes: If you havent already, make sure you do your level 10 conjurer class quest before you make the trip to Limsa(this is another requirement before you can learn to cook or fish - or take on any other class training that might interest you later). And you should be able to unlock the first couple Guildhests now if you really want to get your feet wet in instanced fights with your LS friends(i believe the first 2 were level 10 required). In addition to that, if you havent already its advised to take up the Hall of the Novice training for some basics of how your class should function in a group dynamic plus some decent gear(the actual hall is outside Limsa, but you can get the training from any city - look for a Smith NPC at the inn).

And finally, welcome to the game!

[MistakeNot]

In addition to that, if you havent already its advised to take up the Hall of the Novice training for some basics of how your class should function in a group dynamic plus some decent gear(the actual hall is outside Limsa, but you can get the training from any city - look for a Smith NPC at the inn).

The actual Hall of the Novice is right next to the entrance to Sastasha (the first dungeon) and the MSQ will even send you to visit the hall on the way to unlock Sastasha.
Doing the training in the Hall is indeed strongly recommended. The gear you get is quite good - especially the ring you get for finishing it - and the training itself, while not all that special, can be useful for someone new to MMOs.