You need to go to the Aethertye at the particular camp you have the leve for. As you get near it a small exclamation point icon will appear and you can open you your menu and hit "Aetheryte" this will allow you to interact with it and pick which guildleve you want to complete as well as set the difficulty level (I recommend 1 star if you are just starting)
You wil then have map marker indicating where to go and a kill counter to track your progress. Gathering leves work in a similar manner but it shows you where to harvest instead of enemies.
You should also check out the Lodestone for more information, this link is specifically for the aetheryte but the side bar on the left links to a decent amount of info (with pictures) to get you started http://lodestone.finalfantasyxiv.com/pl/guide/aetheryte01.html