To see mineral deposits you have to have prospect active, to mine you have to have the pickax equipped. They show up on your minimap when you get close to them. So exit Ul'Dah via the Gate of Nald. This should put you in Central Thanalan south of the Black Brush Station aetheryte. From the gate, hang a left and follow the walls and cliffs for a short journey. Before you get to the river in the area of the map roughly near "Stonesthrow" you should find a set of 4 mining nodes, these are your copper ore(and a couple other things). Once you level up this will get easier. At level 2 you get a trait that automatically turns on prospect when you switch class to miner(so you can no longer forget to turn it on). Then at level 3 you get an ability usable every 30 seconds that points you toward the nearest mining node and tells you roughly how far it is.