Welcome to the game, Waldstein.

I didn't do the main storyline in Gridania, so I'm not sure exactly what you're supposed to do. Here's a link to the Eorzeapedia page on the Gridania main storyline quests. Clicking on each quest will give a walkthrough.

As you probably know, the Archers' guild is in Gridania. But are you sure you're not thinking of the "Adventurer's Guild" in Gridania, and not the "Archer's Guild"? There's a desk in the Adventurer's Guild that gives leves, which are like little mini-quests that you can do daily.

If you can't figure out to whom you're supposed to talk, open your Main Menu, and click on "Journal." That will open a list of missions you've currently got. If you click on the individual mission names, it will open a card listing the mission objectives. And down at the bottom of the card is a button you can click for a "Map." That Map will show you where you need to go for the next mission objective. So if there's one person you need to talk to or something, it will be shown on the "Map" that you can look at through the Mission Card.

As for going to Uldah, here's a post I did giving directions from Gridania to Uldah. It links to a couple of maps, so that might be helpful. As Dreamer said, you just need to follow the road South from Gridania, until you get to Thanalan. Then run West, until the road splits. Then head South again, which will lead you right to the front gates of Uldah.

Have fun!