To build the raft, you need lots and lots of wood. When you first start out, your main source of wood will be from the driftwood that floats on by every now and then. Be sure to keep an eye on it.
You can build using one of the two methods: tapping on the blue crystals, or opening the task list at the bottom right corner of the scree. If there is a blue crystal on your raft, that shows that you need to build something there next.
Tapping on the blue crystal will bring up the structure that needs to be built. To access a quick list of the planned buildings, you can tap on the task list. Using the task list is a little faster than individually tapping on each crystal.
For the most part, rafts are what you are going to building most of the time. To be specific, more raft space so that you can build more structures on top.
In order to build as efficiently as possible, you will want to build rafts until you unlock a structure of some sort, like a tree or a carrot farm and so forth. All of these structures boost your overall wood generation rate, making it much easier to earn wood faster in the long run!
Once you build the structure, then you can go back to building more rafts. This way, you will be generating more wood over time that can help you build the rafts faster. It is the ultimate plan to build your raft completely!