To get cobblestone you need a pickaxe. It's easiest to just make a wooden one. Dig down and you should find some rock but it doesn't look like cobblestone. If you mine it with the pickaxe you'll get cobblestone but if you don't use the pickaxe you won't get anything.
The are to ways to get coal. One is to dig until you find blocks that look like rocks with black specks and mine those with a pickaxe. The other way is to get wood and burn it in the furnace. It has to be plain wood and not planks. One more thing, when you are digging, don't go straight down. Go down and forward so it is like steps because if you go straight down you will have a very hard time getting out of the hole you dug.