Diamond is what you are after in the end, and it is often times in some pretty hostile areas. Having an Iron suit of armor on can really help to alleviate some of your worries about dying. Diamond is precious and rare. If you find some, bring it back to the surface before something bad happens.
Don't use up too much of your diamond on tools. Make a pickaxe and sword out of it, but hold off on the others until you have a very large supply of it. The same goes for armor. It takes a ton of diamond to make a full suit, and that can be better used on pickaxes for mining and swords for your defense.
Once you have diamond, mine up some obsidian using a diamond pickaxe. It is typically found deep underground where water and lava have collided. You can build a portal out of it, and using a flint and steel, you can light this portal up and take it to The Nether.
The Nether is like the underworld and is extremely dangerous. It is recommended you leave your valuables at home. Don't bring in Diamond items, because it is likely you will die, and this place is filled will lava.
The Nether is filled with Netherrack and Soul Sand. Neither of which are too useful. However you can also find Glowstone here. Glowstone when turned into a block is one of the brightest lights in game and can light up an area similar to 2-3 torches. Netherrack when lit will burn forever.
After obtaining diamonds and reaching The Nether, the rest is up to you. You have all the major items now at your disposal, so go ahead and build a crazy world. Build houses, sky mansions, crazy mine systems, and underwater tunnels. Connect it all with elaborate mine cart systems and have lots of fun. Remember to light it up with torches though, because Creepers would love to come knock it all down.