Build your base
Gather a significant amount of wood or (other abundant materials. I just prefer wood for a start) to build your home. Then go find a spot to build it in. You can build just about anywhere. But it is preferred to build it near your spawn point. Your spawn point by default is in the very center of the map. You can later change your spawn point by Crafting a bed in an acceptable house and activating it. (Note: If the bed is destroyed, spawn point is reverted back to default)
You will have an NPC around with you. A Guide that can give you random tips to the game. Speak to him to learn various things you may not know. But this NPC, as do many other NPCs require homes so they can move in / respawn if killed. It is advisable to also attempt to construct a house that is elevated from the ground to make it safer for the NPCs. The requirement of a valid house is at least six blocks high and ten blocks wide, has a table (workbench is okay), a chair, a blank spot the NPC can stand in (the portrait of the NPC shows where this space is), fully enclosed (including the background wall which can be built in the Workbench). This is a sample of a simple elevated "apartment"