After you familiarize yourself with Limsa Lominsa and get some experience, Baderon has a job for you.
Starting the Quest
Talk to Baderon in the Drowning Wench to start the quest. The nearest aetheryte is The Aftcastle. Another way to get there is to use an aetheryte to go to the Airship Landing (available after you have attuned to all aetherytes in Limsa Lominsa) and take the lift down to the Drowning Wench.
Speak with Staelwyrn at Summerford Farms
If you have attuned to all of the aetherytes in Limsa Lominsa, you can use an aetheryte in the city to go out of the Zephyr Gate and reach Middle La Noscea. Or if you want to go there on foot instead, the Zephyr Gate is east of the main aetheryte of Limsa Lominsa.
If you have completed your level 1 job quest (which is highly recommended), when you leave Limsa Lominsa, you may see enemies with a target symbol over their heads. You can kill these to get bonus experience points from your Hunting Log. You can review your Hunting Log by choosing Logs from the Main Menu, then choosing Hunting Log. This will show you all the targets in the log, and the experience rewards for each.
Information about Enemies
Enemies with a blue icon next to their names won't attack you unless you attack them. Enemies with a red/yellow icon next to their names will attack you if you are fewer than 10 levels higher than them. Proceed with caution. Enemies that are a higher level than you will be more difficult to kill. If you die, you will be prompted to return to your home point.
Information on Gear Condition
Your gear condition is sometimes lowered after you kill enemies, and is also lowered if you die. You won't lose your gear if its condition drops to 0%, but you will no longer receive the stat bonuses from it, so until you repair it, it will be as if you're not wearing it. There is a mender in the marketplace who can repair your gear for a fee.
Go to Summerford Farms
Once you are in Middle La Noscea, check your minimap for the green check mark symbol, and go that way until you reach Summerford Farms. If you see enemies with target symbols or quest symbols over their heads, be sure to kill them to make progress in your active quests.
At Summerford Farms, go up the winding path up the hill and you will find a large aetheryte crystal. Attune to it. If this is the first aetheryte outside of Limsa Lominsa that you have attuned to, you will learn the Teleport spell. You can use Teleport to go to any of the large aetherytes that you have attuned to. However, it costs gil to use the Teleport spell, and you probably don't have a lot of gil right now, so you might not want to teleport anywhere just yet.
Talk to Staelwyrn
On the top of the hill, go around to the other side of the hill to find Staelwyrn. Talk to him, and there will be a cutscene. After the cutscene, you will be prompted to complete the quest. However, the Complete button will be greyed out. To fix this, you need to select one of the items listed under "Options" to the right of the experience points in the window. You can choose Altered Thighboots if your job is a Disciple of War job ("Disciple of War" will be red if your job is not a Disciple of War job). Otherwise, you can choose Altered Leather Thighboots, or gil (which you can sell to NPC vendors for money). Once you have selected your reward, you can click the Complete button to complete the quest. If you chose one of the pairs of boots, be sure to go to your Character window (under Character in the Main Menu) and equip the gear. You can click the Recommended Gear button above your character's image to let the game automatically select the best gear for you from the items in your Armoury Chest. The Recommended Gear button won't select anything that is in your Inventory, so be sure to put gear in your Armoury Chest by opening the item's context menu and selecting Place in Armoury Chest.
Next Main Scenario Quest
After completing the quest, you will need to be at least level 5 before you can accept the next quest from Staelwyrn: Dressed to Call.