Most people regard sake in the same category as other spirits like whiskey, vodka, etc. It is more akin to beer though. Even though it is similar to beer, the process is much different and far more complex.
Historically, people have made alcohol out of whatever was readily available, and in the case of the Japanese that was rice. The modern process for brewing sake involves getting and cooking white rice. This process is highly monitored and controlled so that the rice is perfectly cooked at the end of the process.
The interesting thing about rice is that it doesn’t contain amylase enzymes, which are the enzymes found in the malted grains used in other spirits around the world, so there is a mold called koji mold that is laced into the rice that performs the same task as amylase. After the rice has cultivated an appropriate amount of the mold it is mixed in stages into a vat with water and yeast. By adding the entire batch in a staggered manner, it allows the yeast to work more efficiently, keeping up with the increase in volume of food.
Once all the rice is added, the mixture (known as mash, or moromi to the Japanese) is left to sit for several weeks at which time the liquid is seperated from the solids, pasteurized, and left to mature. At the end of this process you end up with a naturally fermented 40 proof beverage that is then diluted down to around 20 to 30 proof, bottled, and sold worldwide.
The maturation process is a fairly new addition to the process of making sake. Maturing the sake is what mellows the flavor, moving it away from the rough, harsh flavor that was so prevalent historically. Thanks to the invention of pasteurization, sake has a longer shelf life and brewers can afford the time to mature the sake before shipping it.
So that’s how you brew sake. It may not seem that complicated, but there are a lot of subtleties that go into each step that make the process more difficult. That being said, it’s possible to homebrew sake and it isn’t terribly difficult (more difficult than homebrewing beer, but less difficult than distilling spirits at home).