Find a house the first night or two, create frames to block windows and doors. First couple days is generally spent gathering food, water and supplies.
Decide where to build a more horde-safe place. The first horde is on day 7 at 22:00. Zombies and Zombie Dogs can beat or chew through wood fairly quickly so building a base of wood with little or no defence is not the best idea. A rooftop fort is better. Gather tons of wood. You will need it.
If you choose to build a wood house, then the house itself isn’t as important as the defenses around it. Wooden spikes is the cheapest defense to build and doesn’t require special tools. It takes 4 wood for a one-block size set of spikes. As the spikes take damage, they will become more ‘bloody’ looking. They can be destroyed completely. Take care when moving around spikes, they cause bleeding and can kill players. Wood Log Spikes last longer than Wooden Spikes but take more materials to build and do less damage.
Cobblestone can be created by low level players and is more durable than wood. It requires wood, fiber, stone and clay. Wood and Fiber can be gathered by hand, but stone and clay require mining. A pick or shovel are the best tools for this job but may not be accessible to players just starting out until they have crafted a forge for smelting iron. If you are building a base rather than reinforcing an existing structure, start by creating four towers, each in a corner of a 5 x 5 space. The bottom platform of the structure should be out of zombie reach. Use frames if needed to create stairs while building to get your character up higher till you have your towers as high as you want them. Build towers between two on two sides to put ladders on. Zombies cannot destroy them so wood is fine.
Once this is done, create a floor and build on top. This should protect you from all zombies except the Spider Zombie, who can climb up walls. Placing a one block wide wood ledge around the platform will stop them as they can’t get around it. Do not build past the towers as you risk the entire thing collapsing from displaced weight. Place defenses around the base on the ground. For a stronger base, consider building on an asphalt roadway. It’s not recommended to build on or near farms. Yes it’s nice to have a pre-made garden but zombie dogs love them too and are very aggressive. They will chew at the base of structures.
Probably the safest place to build is on the roof of a brick building or deep in an underground cave. Zombies will ignore players at a specific distance. If you build on a roof and use a ladder, remove the last bottom section of the latter, players can still get up it but zombies have a harder time.
For players choosing to build underground, there are a few things to keep in mind. The biggest one is physics. It’s real and it will kill you. Having a tunnel collapse is not fun and depending on the material and amount falling, will most likely kill you. The best bet is to find a mine that already has tunnels naturally in it. Unfortunately, these are rare in-game, at least on the current maps. Caves are cool though and some have natural water pools, saving you from having to building a cistern and bringing water in using the Water Bucket.
Other things to be wary of are heat and activity. Items such as Forges and Torches create heat and this in turn will spawn Screamer Zombies. Screamers will spawn smaller zombie hordes if not killed immediately. Never place your forge near the entrance of your cave or If you choose to dig your own cave and tunnel system, start by digging a 3 block deep hole, then go downwards at an angle and decide at which depth to create a cave. Alternatively, you can dig straight down, but you will need to place ladders to get back up. If desired, place a hatch at the entrance.
By looking at your map, you can see your current depth. Bottom is at - 56 and is covered in Bedrock. When struck with a tool, it will make a ‘twang’ sound. It is possible to hit water on the way in and a detour will be required. Natural pools are nice as a water source, but a cistern can be created and filled using blocks and the Water Bucket. Defenses are not necessary deep underground but zombies can dig so having your cave carved into a hillside is not a good idea. Go for deep underground. Digging in a North, South, East or West direction using your compass will give you a better chance of having straight lines.
Once you have your cave where you want it, and it’s a good distance from the surface, use whatever materials you prefer but reinforcing cave edge walls with concrete or cobblestone is a good idea. If you build a multi level domain, use towers for stability. Be sure to go back up and place defenses on the surface. Gardens will not grow without a light source, so they will need to be above ground, or in a connected pit with frames above to keep zombies out. Light will flow through frames.