The best way to start a base is simple, just find a berry bush near some trees and start a campfire. But more advanced players have access to more materials used in making a base, so they may be able to create a better working home.
The easiest place to start your home is in the bottom left or top left corners. There, you will already have two walls of your base complete, and wide access to wood. This will help you while making further supplies. An important precaution while building in a corner, though: watch out for wild animals. In your spot, these beasts can easily corner you and make you their dinner. Also, too many players kill resources and add danger to the neighbourhood.
To start your first base, set yourself near a berry bush, but be careful to claim your corner. Once you have enough supplies, move into your corner and begin the construction. Start off with walls and or spiked walls in the middle, for this will give the most defence, and lay out how big your base will be. From there, build out. Do not forget a door though - put it in a corner near the tree line, this will provide the most shelter for it.
Once you have completed your first wall, begin working on a second, stronger one (stone, if wood is your first, gold if stone is your first, and so on). This will allow you to destroy your first wall with a hammer later on, and have more room to move about.
Now, for the inside. The easiest design is simple: fire in the middle, bush to the side, and maybe a workbench for crafting. More advanced players can add chests to store supplies, preferably with a lock to be safe, and a furnace, which acts as a renewable heat source. You can also add man-made bushes with seeds, but these will die quickly, especially if they are harvested by tools instead of hand. Be sure not to depend entirely on these planted food sources. If you want to start a clan with other players, place down a totem, but make sure to keep it protected - unless if you want random strangers to be able to join!