The first thing I do is find cows and kill as many as possible (get a stack & a half of raw beef and around 50 or so leather). While I'm killing cows I'm also on the lookout for sugar cane and gather as many as I can while I'm killing the cows. Then I make a makeshift shelter and a makeshift sugar cane farm, nothing too crazy at the start.
Then I either find a cave system that goes down to diamond level or dig down to level 10 and start a branch mine system. I only collect 5 diamonds and leave the rest of them until I have a fortune 3 pickaxe. I mark out the entrances of my branches with signs telling me if the branch has diamonds, leads to a deadend (lava), or a cave system. Then once I've collected my initial 5 diamonds I make a diamond pickaxe and collect 4 obsidian. Between killing cows, smelting iron, and collecting coal I should have close to 30 experience levels to enchant that diamond pickaxe. Go up to my makeshift shelter and make an enchanting table and 15 bookshelves and pray that my first enchant is a fortune 3 pickaxe so I can go collect all those diamonds that I've marked out. If not I go down and keep mining coal and redstone (leaving the diamonds alone except for another 3 that I'll use to make another pickaxe) until I have enough experience levels to try again.
That is general start up that I use for every map on any difficulty level. A lot of people use the leather to make leather armor for the beginning stages but I think that's a waste because you can have full iron armor pretty quickly starting out like this and you save that leather for your books that you'll need to make your shelves. Plus branch mining is relatively safe as long as you light up your tunnels and are cautious of lava.
The step, for me, after forming a shelter... is to start a wheat farm. In survival, you need a sustainable food source. There's no other option at the beginning or in early game. I always try to form a shelter near a water source for this reason.
1. Punch wood, make wooden pickaxe, mine.
2. Get 3 cobblestone, throw away pickaxe, make stone pickaxe.
3. Get coal, make set of stone tools and a furnace while killing animals for food.
4. By then it is usually the end of the day and I always have at least 10 pieces of food, enough iron for a pickaxe, coal, and stuff.
6. Explore more.
7. Fall into some epic cave and mine it all, this is the second day of minecraft, should have iron tools and armor by now.
8. Go to surface, about 7 ingame days have passed.
9. Make house.
10. Make farms.
11. Mine for diamonds.
12. Make diamond pickaxe, mine obsidian.
13. Make enchanting table, enchant armor and tools, go to nether
14. Come back form nether, make brewing stand and netherwart farm.
15. Mine more, get around 40 diamonds, make set of diamond tools and armor.
16. Enchant them all with lvl 30 enchantments.
17. Put them somewhere, make fire resistance potion.
18. Go to nether, drink potion at nether fortress, farm blazes.
19. Get a bunch of enderpearls.
20. Wear diamond armor and tools, bring enchanted bow with a lot of arrows. Go to stronghold and defeat enderdragon.
21. Go to nether, stay in fortress until I have 3 wither skulls.
22. Go far from home, defeat wither.
23. Make beacon.
24. By then I would have deleted my world and made another.
If that means You've Gone Caving ang Got Some materials. Then what I would Do is Create Large Scale Farms like in Episode 6 Of My Lets Play Series. (Soon To Be Posted). If you want to see what I mean Check it out. Or I would Take 50 Minutes To Do This: