Well, going by the gear shown for your character on the Lodestone, it appears you've at least gotten through some of the first set of dungeons, so you must have played together with a group at least a time or two when you earned those Acolyte's gloves and boots. So, you're a level 23 thaumaturge, and somewhere in the level 16-20 range on where you're at within the Main Scenario quests.

As for not knowing what you're doing apart from quests and such, the quests themselves (particularly the Main Scenario ones with the flaming ring around the quest icon) should lead to and introduce most of the other activities in the game, just as they led you into doing dungeons when a quest told you to go into Sastasha. Once they've been unlocked through their corresponding quests, dungeons can be repeated by selecting them again from the Duty Finder, and they're a major source of the content people run together in groups.

If you want to make friends and play together with people you'll come to know, rather than with whoever is randomly selected by Duty Finder, your FC should be a good source for that. Ask in FC chat if anyone wants to run some of the low-level dungeons together. Invite whoever agrees to your party. (Duty Finder is still used to actually enter dungeons even if you're not using it to find you a random party. If you put a party together yourself and then join a dungeon in DF, your party will go into it together.)

Does your FC hang out at your FC house much? If so, that's another place you can get to know some of them in a non-dungeon setting.

Use chat to get to know people, and in the meantime, continue going through the Main Scenario quests to both see the game's story and unlock more of its content. Also do your class quests each 5 levels.



Not sure what mechanics are still new to you, so just in case:

FC chat, party chat, etc.:
There are two ways to specify which chat channel you want to use. You can click the little button at the bottom left of the chat window (the one with the dialog-bubble icon) to get a list of channels and select the one you want. Or you can prefix what you want to say with a slash and the name (or abbrieviation) of the channel. For instance, typing "/fc hello everyone" will send "hello everyone" to the members of your FC, while typing "/p hello everyone" will send it to members of your party.

Inviting people to a party:
You can either select a player character when they're in front of you, select their name from the chat window, or select their name from the search window. Right-click on them if you use keyboard/mouse, or select them and press the square button on a PS3/PS4 controller to bring up a list of available actions, and one of those actions is "Invite to Party".