A little tip for mining from the very start; if you want to go mining, prepare for dangers such as long drops, scorching lava, and those who lurk in the dark. Bring lots of armor, picks, swords and courage.
Mining is a fun yet dangerous thing. I'll start you off with a few materials you should have:
Now when mining, you'll want to start your shaft close to home, and in a large, promising mountain. Waste no time digging sideways, what you want is down. Gold and Diamond tend to be very close to the Adminium Floor, and you'll want to be as far down as possible to increase chances.
Return to the surface often to resupply, and do not fear the dark. Light your path. My brother experienced this the hard way; he dug for diamond using minimal torches. After getting deep, it was dark enough to spawn a Skeleton, which swiftly killed him, and you, like him, will be much to far in to be able to reclaim your items before they despawn.
If you cannot find diamond, do not feel bad to abandon a mine. Some mountains have diamond, some do not. Don't give up too easily though.
And RULE NO.1: Always, always, ALWAYS mark your mining shaft. You do NOT want to forget where it is, or fall down it during a Creeper chase or something.