OK, this is a new video that will help you understand how mining on FFXIV works. In the below video the player is on a quest that requires him to gather mined items.
Mining is done through a skill based menu. Once you start to attempt to mine a circle will appear on the screen.
An inner ring grows from the centre of the circle and with a timed button press you stop the growth of the ring. It looks like you want to get the inner ring as large as you can without it growing bigger than the circle.
After the first attempt the inner ring shrinks a little, then the next attempt repeats the process but uses the shrunken ring as the maximum area the next ring can occupy.