It Peista to Listen

http://ffxiv.gamerescape.com/wiki/It_Peiste_to_Listen

When in Western Than, there should be a green circle on your map. Head over there and open your Journal. Click on the levequest and then click "Initiate".
Then just mine until you're done. Botanist and Miner leves all work like this, sometimes you have to collect a certain item within the nodes, other times you have to just hit each node...
For fishing, they are all turn ins.

When done with the leve, head back to the levemete (or accept the teleport) and turn it in like you would a battlecraft leve.