Mobs spawn in dark places so your gona need some torche just get some coal and sticks. Swords are for killing things, pickaxes are for mining, axes are for wooden things, and shovels are for digging
Hope I helped
I agree with pretty much everything said here. Zombies and skeletons won't go through doors though (as there's no iron doors yet in MCPE). Swords for killing, pickaxes for mining, axes for chopping wood, shovels for digging dirt, and hoes for gardening and tilling the dirt to place seeds for crops.
Also, for coal, if you can't find any, make some. Simply make a furnace (need 8-9 cobblestone), and burn some wood in there. You will have made your own coal.
On a side note, you will want stone/iron tools, those generally work best. Unless you're lucky and find diamonds, those are the best to make tools from.
As for the zombies in the mine, it may be there's not enough light in a certain area in the mine where they spawned from. Try and place torches in all the dark places, I tend to space my torches 5-6 blocks apart from each other.
Just some extra advice given to what's already here.
It's in the crafting table. It will be under the section that has the pickaxe/sword. Arrow is at the top of the list (it has a bit of a shadow over it), unless you have the right ingredients. You will need 1 stick (made from a wood plank block), 1 feather (zombies and chickens drop them once killed), and 1 piece of flint. Flint can be found when digging through gravel in mines or on land.
Also, arrows will be dropped by skeletons, so if you can't make any just yet, try to kill a few skeletons with a sword and you will be able to get a few.