As far as learning a new class (including crafting) goes, first you'll want to do your level 10 class quest back in town (You receive class quests every 5 levels from your guild, up until 30 when you get the job questline). Once you've done this, you unlock the armory system. Then you just go to any guild (such as the blacksmith guild in Limsa Lominsa,) talk to the receptionist at the desk, and sign up to join the guild. This will give you the first class quest for that class, as well as a level 1 weapon/tool for the class.

To change classes, it's as simple as equipping a weapon/tool you have the level to use. So equip that level 1 hammer and you get to start up blacksmithing. Do note that, unlike other games, crafting and gathering professions in this game are full fledged classes with quests and gear that must be upgraded.

Finally, I do recommend that IF you start crafting and gathering, that you wait until level 15 when you can use airships, then get all the crafters and gatherers and level them up equally. That way you can get any materials you need yourself, and also until level 50 every single crafter uses the same armor and every single gatherer uses the same armor. So instead of having to get the same armor every time you get a class in the right range, you can just use it on all the people who need it before getting rid of it.