It's important to gather enough food during the day to last you through the night. Try harvesting tall grass for wheat seeds, sugar cane for sugar, and animals for raw meat. Seeds and sugar can be eaten directly. Also, if you find some clay you can use it to make a small oven (it can only burn sticks and other small sources of fuel) and cook the raw meat, doubling its nutritional value.
Be sure to make a shelter before nightfall, and start building it well before dusk. Sand blocks are useful for making the walls of your shelter because they are easier to harvest than dirt.
After you have built a shelter and stockpiled enough food to ward off immediate starvation your next priority should be making tools to increase your harvesting ability. The flint hatchet is probably the first tool you'll want to make because it will allow you to harvest logs. It requires a piece of flint and two sticks, and can be made without a workbench. The flint can be obtained by digging through gravel blocks (they often drop flint or flint chips) and the sticks you can get from harvesting leaf blocks. Sticks can also be found occasionally lying on the ground in forested areas. With a hatchet you'll be able to chop down trees and use the wood from them to make a workbench.
Once you get a workbench try making some shovels so you can dig through gravel more efficiently. This will provide you with more flint to make another hatchet or axe, and you'll also start collecting metal nuggets which you can combine to form ingots.
Upon obtaining 3 ingots of the same metal you'll want to craft a pickaxe so you can begin harvesting metal ores. Keep in mind that smelting common metals requires at least a stone furnace burning coal. You can convert gravel into cobblestone for the building of the furnace.
Wielding a stick or bone gives your character a bit more reach when attacking animals and mobs.