The entire clicking the ground tile thing is something similar to H&H. Just an easy way to cross over mining on a basic scale the original developers knew. :p
Onto point.
Tea is recommended when mining but not required to be resourceful. You can quite easily forage a few hundred crabs and cook em' up to mine for a few hours quite easily; not to even mention the amount of game meats you can bring back and also use that would otherwise be better composting material.
You will start with a stone axe. This is very important to remember as it'll dictate how much time you waste. There are two options from this point:
I. Mine in a straight line and give no ***** about cave ins to find iron ASAP. Once you do make a metal shovel from your smelted pig iron.
II. Buy a god damn pickaxe. It might be expensive to new miners but really this saves you a lot of time. If you find a good deal on a steel pickaxe go for it as well as steel is being cut in price everywhere if you look in the right places.
You will also want to invest in either a cart of a sled. Any version of either is fine as half the process of mining is quite simply breaking down rubble boulders and shifting them in a stream near your house. Avoid shifting in town as I make it a tradition to push auto-shifters out of the river. Doing it on a piece of claimed shallow water is better as it is quickly used.
Above all I'm going to recommend one thing and one thing alone. Get some shrubs of berries and tea up and going, at least 50 to 100, to make mining anytime you want less chore like in the food gathering department. Sadly this is not H&H where you can bring a cart filled with beer barrels. : )