Now that you are familiar with the various items that you can craft using the resources that you have added as your goals for the first two days of play, you should at this point have the basic Stone Tools, you should have a shelter with a door, and you should have torch light inside and outside of your home.
Now it is time to begin the quest for new resources, and the most efficient (not to mention the safest) way to obtain this is to start out by creating your mine from inside your shelter. Seriously. This is best accomplished by digging a set of steps down ten or so blocks deep then a hall that you can set up a door in, and make very well lit so that nothing will spawn there. That gives you a safe entrance to use to seal off your shelter from the mine, while at the same time offering you direct access to your mine that does not require leaving your shelter into the overland, where Creepers and who knows what else can get at you!
Sand is found along the water and is useful for making Glass
So start off by making sure you have an adequate supply of wood - which does mean venturing out into the overland to harvest it. Three or four stacks of 64 Wood Blocks should be plenty. You don't have to worry about stone, you will be obtaining more than plenty of that as you dig.
The odds say that it is going to take you around four days (maybe more) to get the Wood you need, which is why this section spans that period. If you are faster at it, good, otherwise don't worry too much about it, especially when you consider that you are still getting used to the controls in the game.
While we are on that subject, once you make some Chests you will need to learn how to move things in and out of them. That is accomplished by tapping on a Chest to open it, at which point the game will produce a menu with your Inventory and the Chest side-by-side.
You have two methods for moving items into the Chest - tap the item from your Inventory to move just one item, or press and hold the stack to move all or part of it - how much is communicated by the bar that slowly fills on the stack you are moving.
While it is awkward you can also use the Chest to re-arrange stacks in your Inventory by moving them back and forth, since the game automatically placed items in your Inventory in the next available open slot.
You will also notice that adding items to the hot bar for your use is accomplished by tapping the item or stack in your Inventory.
After you have the stacks of wood you need, make some Stone Picks and then begin excavating through the back and the floor of your shelter to create the entrance hall to your mine. It would be an idea to go down around ten blocks and then make a hallway that is ten blocks or so deep, and three wide, then craft a door, then build a wall in the hallway and place the door in the center. Doing this ensures that your shelter is a safe area no matter what happens when you are mining - for example you have the bad luck to tap into a cavern full of monsters, well then you have someplace to run to!