Minecraft wiki entry for The_second_day, associated text: Keep track of where you are, using the debug screen by pressing F3 if needed.
If you do get killed at this point, you haven't lost much, and you're presumably still near the spawn point. Just head back to your death location to collect your items within 5 minutes.
Collect any loose items you see, including but not limited to: bones, arrows, rotten flesh, eggs, and ink sacs. Almost everything becomes useful later.
Destroy any tall grass you see and collect the seeds they drop.
If you see chickens, hold seeds in your hand to lure some home. If necessary, just stuff them inside your house until you have time to build a proper pen. Save the eggs for later.
If you find mushrooms, break and grab some of them. If you can get both kinds of mushrooms, you can make mushroom stew. You might also collect flowers for the dyes you can make from them, or decoration. Flowers have another use too, but this isn't useful for now.
After chopping trees, collect the saplings (and perhaps apples) that drop from the leaves.
Mine any iron ore you find with a stone pickaxe. Using a wooden one causes it to mine slower and not drop anything. Also mine some of the coal ore.
As you're moving around the area, keep an eye on how the ground rises and falls. Over time, you may be fencing off more and more territory to keep monsters out, starting with the area right around your house (or cave entrance). If the terrain is uneven, you'll probably run your fences along ridges, avoiding places where mobs could jump over the fence from a hill or cliff.