The First Night
You've spawned! Look around you. Is the landscape sandy, with gentle hills? Is it bright green, with large trees soaring above you? Is is green with sparse trees? Is it covered with snow? Is the ground purple with red cows around you? No matter where you are, seek the nearest trees. Jungles, forests, and taigas should be your best bet. Grab 8-12 pieces of wood. Open your inventory, put them in the crafting grid, and get wood planks. Use four planks in a square to make a Crafting Table. Put the table down, make sticks, and make a wooden pickaxe, sword, and maybe a shovel. Now go in search of coal. If you find some, great! Get it! If there is none in the immediate vicinity, get some stone. That should be easy enough to find; just find a hill or dig down three or so blocks in a staircase pattern- never, ever dig straight down! You will want at least eight. Craft a Furnace. Put the logs in and smelt them however you want to make Charcoal. Then, Charcoal or Coal, get some sticks. Put the coal on top of the sticks in the crafting grid to make torches. By now it should be about 2:00 PM, Minecraft time. Dig out a hole in a mountain (or if there's a village close by, shelter in the houses there.) and light it with torches (or dig down a few blocks and light it). This will be your shelter. Stay near it. You're now ready to survive your first night. Hint: put a one-block window in your shelter, but stay away from it, as Skeletons can shoot you through it. Creepers can also wander up to it and explode if you're near enough.
The Second Day
Once the sun is well above the horizon, emerge from your shelter. If you see hostile mobs, go back in. Avoid foresty areas where the two aforementioned mobs may hide from the sun. When you're still at home, check the area. Any Creepers? If so, either get out and kill them or run away. You can leave Spiders alone unless you want String (for bows or fishing rods) or Spider Eyes (for brewing and a last resort for food). Your job right now is to get food. If you feel like gambling, chop down an oak tree with an axe (you can easily craft one). After you do that, search under the trees with at least some armor and a sword. Kill any zombies you find in hopes that they drop Iron Ingots, Carrots, or Potatoes. The latter two are good food sources. If you don't feel like gambling, the easiest food source right now is probably meat. Kill farm animals to get it. Steak (Cows) and Porkchops (Pigs) are generally the best, but Chicken can suffice as well. While you're at it, if you want a bed, kill some Sheep for wool-or, if you've collected enough String, just use that to craft wool and a Bed. You also want to start a farm now. Break some tall grass. This should get you a few seeds. Make a hoe and till some dirt (preferably next to water; chances are you won't have iron yet, but if you do, you can make a bucket). Plant the seeds. Soon, they should grow into Wheat. By now, the sun might be getting low. As a last-minute precaution, place Torches all around your home's general area to stop mob spawning. Then run back into your cliffside cave and wait out the night, preferably cooking any meat you gathered.
The Third Day
Go through the same safety procedures before leaving your shelter as you did yesterday. This should become regular. It's time to move out of your cliffside cave and make a more permanent base. A simple house or sky base is good enough for now; get some Cobblestone and just build a simple cube (5x5 on the inside is fine). Move in your bed, chests, crafting table, and furnace(s). This will be your temporary shelter before you can build something bigger and better.