Hello Everyone - New player here!

[Enkidoh]

Welcome to Eorzea!

You are correct, FFXIV has what is called the Armoury System, that allows you to switch between classes on the one character simply by equipping a weapon or tool. However, before you can do so, you have to first level your starting class to level 10, and then do the quests given by your starting class's Guild up to the level 10 one (in your case, the Archer's Guild in Gridania).

Once you've done the level 10 class quest, the Guildmaster will tell you that you have been given leave to try your hand at other classes, and it will tell you 'Armoury System Unlocked' in big letters. You then have to go to each class's Guild and sign up there by speaking to the Guild receptionist, and then the Guildmaster (the Guilds for each class can be identified with a sign outside that shows the icon for that class), and you are given a starting weapon or tool for each to equip.

Then, just open your character menu and click on the weapon slot, and then drag on the weapon or tool of the class you want to switch to, and place in the slot. You'll instantly change to that class, albeit you will be back at level 1 with no EXP and have to level it seperately (each class has it's own EXP bar to level).

If you have any further questions about this or anything else, please ask!