Minecraft wiki entry for The_third_day, associated text: Start a farm of some type to always have food and other materials on hand, such as a wheat farm.
Start a mine down to the bedrock, create a mineshaft if possible, and stockpile ores.
Craft a Book and Quill to jot down important coordinates and keep it on you as an alternative to maps. Some players use text files in their PCs in place of this.
Make a mob trap and get resources (gunpowder, string, arrows, etc.)
Return to your home and further expand it and craft new items.
If you go mining and see lava, gather it with an empty bucket:
Lava buckets are a very good fuel source – they can smelt over 100 items per bucket. However, be sure to empty the furnace, as once 64 items are smelted and they are not removed, the furnace will still be using up the fuel but will not smelt anymore items. Just take the output stack and refill the input stack, and the furnace will continue until it runs out of fuel. Later you can make hoppers to automate the flow of material. This is especially useful if you are making smooth stones in quantity.
With care, lava can also be used to fend off monsters, flooding a hillside or filling a trench to burn them. Try not to start forest fires!