After you join the Adventurers' Guild, you need to familiarize yourself with the city.
To unlock this quest, you need to complete Coming to Gridania/Coming to Limsa Lominsa/Coming to Ul'dah first.
Start the Quest
To start the quest, talk to the leader of the Adventurers' Guild in the city you started in. A cutscene will play. After the cutscene, if you started in Limsa Lominsa, you need to talk to the nearby NPC with the exclamation mark icon over her head, to start the Making a Name quest. After this, you will be able to see and interact with other players. Visit the Interacting with Other Players page for more information.
This quest has three objectives, which you can do in any order.
Attune to the Aetheryte
One objective is to attune yourself to the main aetheryte of the city. Click the quest objective to show its location on the map. Your minimap will also show arrows pointing to your current quest objectives, if they are in the same area that you are currently in. If the current quest objective is in a neighboring area, open the map to see arrows pointing to where you need to go to move to that area.
Go to the aetheryte (if you find a line of blue/white pentagons in your way, just walk through it to go to the next area) and check on the aetheryte to attune with it. This will teach you the spell Return. The Return spell will return you to your designated home point (which is set to your starting city's aetheryte by default). However, you have to wait 15 minutes before you can use it again, so keep that in mind.
Return is automatically put in your hotbar/crossbar, but if you ever can't find it, go to the Character menu, choose Actions & Traits, select General on the left, and you will find the Return spell there, which you can drag with a mouse into your hotbar or use the controller to open the context menu and assign it to your crossbar.
There are smaller aetherytes throughout the city. Be sure to attune to them if you see them. Once you attune to smaller aetherytes, you can quickly travel between them by checking on them or by checking on the city's main aetheryte. After you attune to all of the smaller aetherytes, a message will be displayed, telling you that you have attuned to them all.
Visit the Guild of your Starting Class
Another quest objective is to visit the guild of the class you chose as your starting class when you created your character. Click the quest objective to display it on your map. If you find a line of blue/white pentagons in your way, just walk through it to go to the next area.
At the guild of your starting class, talk to the NPC with the meteor symbol over their head. After their explanation of the guild, there will be a blue quest symbol over their head. Blue quests unlock new features of the game; you will see them in different places as you progress through the main story. It is generally a good idea to do all the blue quests you find.
Job quests are always listed below the current or next main scenario quest in the corner of the screen, so if you're ever not sure where to find your next job quest, click it to display it on your map. (If there is no job quest listed there, you may need to level up the job more.) Always do your job quests! Some of your job's abilities can only be unlocked by doing your job quests. Also, completing the level 10 job quest will allow you to unlock other jobs. After that, you will be able to freely switch between jobs at any time.
Listen to an Explanation of the Markets
Another objective is to go to the market area and get an explanation of the markets by an NPC there. You will need to hand over an item to proceed. With a mouse, you can click and drag the item from the Key Items window into the Item Request window, or you can right-click the item in the Key Items window and choose Hand Over. After you have selected the item, click the Hand Over button to hand it over. Afterward, there will be a cutscene.
There are various vendor NPCs in this area that you can purchase better gear from, as well as other important items to help you in the game. Vendors are marked on the map by brown sacks.
Return to the Adventurers' Guild
After you have completed the three quest objectives, go back to the Adventurers' Guild and talk to the guild leader. There will be a cutscene.
Level Up to Level 4
Before you can proceed with the main scenario quests, you will have to level up your starting class to level 4. Before you start leveling, you might want to go to the marketplace and purchase some Buffalo Milk from the Tradecraft Supplier NPC. All foods in the game give a 3% increase (a.k.a. buff) to experience point gain, and Buffalo Milk is the cheapest food you can buy. At low levels, 3% is not very much, but it will become more helpful as you level up. The food buff lasts 30 minutes, and you can eat a second serving to increase the food buff to up to 60 minutes.
When you are ready, you should go to the guild of your starting class and do the blue quest there if you haven't already. This will help you level up quickly.
Next Main Scenario Quest
If you started in Gridania, your next main scenario quest is To the Bannock. If you started in Limsa Lominsa, your next main scenario quest is On to Summerford. If you started in Ul'dah, your next main scenario quest is We Must Rebuild.