Depending on your city you'll find "Guilds" to join around the city. Just open up the main menu while in town and look for the map option. You'll see places listed with (Insertclassname) Guild on the map. Go there to buy a weapon to change your class. Unlike previous FF titles, what you equip determines your available skills and abilities. For classes like Alchemy they can mainly be leveled for free by using a Guildleve designed for your class (You can find these at the Adventurer's Guild in any city.) and accept it. Then go to a camp and talk to the NPCs there to start it. Alternatively, buy some equipment to harvest, mine, or fish and collect the ingredients to level Alchemy on your own. Either way it's gonna require you take on performing synthesis recipes to boost your Alchemy levels, throwing rocks at enemies even if they do manage to kill it, won't net you points to level it, only your physical level.
Edited, Sep 3rd 2010 6:58am by SamusKnight
FINAL FANTASY XIV Roleplayer
Sair Gammonari - Hyur Midlander Male - Conjurer (Somewhat retired.)
Mihana Zhralyia - Miqo'te Seeker of the Sun Female - Archer