Alcohol
Alcohol is one of the first ways to produce consumables with potion-like status effects, but with the risk of overconsumption. There are several varieties of alcohol to procure, from red & white wines, to lagers and ales. Each type of alcohol provides a unique effect - there is an official spreadsheet documenting all of this here.
Instruments
Kettle
One will need a Kettle in order to draw out the liquid from our grains. A kettle is made with four ingots of any generic metal and one of any kind of metal bars (like iron bars). A kettle needs a heat source under it running in order to start cooking. For the early game, a furnace under the kettle should be fine, as long as you're cooking something in the furnace. The kettle also has many culinary uses, from stews to mochi. For the purposes of boiling grains, it is imperative not to pour water directly into the kettle - doing so will make it impossible to retrieve the wort. Instead, place bottles of water in the side bar of the kettle, and your grain in the 3x3 table - it will cook into bottled wort and byproduct, making it easy to pull out and use in the Fermentation Barrel.
Mashing Tub
The Mashing Tub is where fruits can be mashed into fermentable liquids. Making this tub only requires two generic metal ingots, along with some blocks and slab of wooden planks of any variety. To work this tub, right-click your fruit into the tub and then repeatedly jump on it. Each jump will consume one instance of your fruit to produce a quarter-bottle's worth of liquid. Once you have finished mashing, simply use a bottle or bucket to pick up the liquid. It should be noted that at this time, it is uncertain whether these liquids will take in the Fermentation Barrel, perhaps another editor could confirm this.
Culture Jar
The Culture Jar is used to capture Brewer's Yeast (as well as other varieties) for use in the Fermentation Barrel. It is made with seven glass panes and one wooden plank1. To use, simply pour in one instance of fermentable liquid, preferably unfermented, un-hopped ale. In most scenarios Brewer's Yeast will form after some time, but depending on the biome, one can procure a special yeast from the jar. Lager Yeast may show up when the jar is in cold biomes, Etherial Yeast when in magical biomes, and Origin Yeast when in mushroom biomes.
Fermentation Barrel
This is where the base liquids (like Apple Juice) will be turned into alcoholic beverages. To use, simple right-click the barrel with the fermentable liquid of your choice and it will be transferred into the barrel - right-clicking again will extract it into your bottle or bucket. The Fermentation Barrel can hold 16 bottles (or four buckets) worth of liquid. To start the fermentation process, right-clicking the barrel with nothing will pop up a UI showing how much liquid is in the bottle, a progress bar, and slots to place in reagents. For beers and (maybe?) rice-wines, Brewer's Yeast will start the process if there's enough liquid; it may require nether wart to produce fruit-based liquors. Ideally, the barrel can be completely full and only one Brewer's Yeast is necessary to ferment the entire barrel. The process will take a while, at least an in-game day's worth of time.
Alcohols
Ale
Ale is produced by cooking wheat in a kettle with bottles of water. When doing this, chaff will be a useless byproduct. Ale can then be re-cooked in the kettle's sidebar with hops to hop the ale, which provides additional benefits when fermented. Ale can be fermented in the Fermentation Barrel with Brewer's Yeast.
Lager
Lager is produced by mixing Lager Yeast with un-fermented Ale. Like Ale, Lager can then be hopped and/or fermented.
Sake
Sake is produced by cooking rice in a kettle with bottles of water. When doing this, cooked rice will be an edible byproduct. Sake could then be fermented in the Fermentation Barrel (have not yet confirmed).
Mead
At this time, it is uncertain how to produce mead must or any variant of honey-based alcohol.
Cider
Cider starts with mashing apples in a Mashing Tub, which produces Apple Juice. Doing this will provide Apple Pips, which can be replanted to grow Apple Trees. The Apple Juice can then be fermented in a Fermentation Barrel with Brewer's Yeast, producing Apple Cider.
Wines
There are three types of grapes to produce wines from: Red, Purple, and Green. The seeds to these grape must be found in dungeons and the like - grapes themselves cannot be turned into seeds. The grapes can then be mashed in the Mashing Tub to provide their respective juice. At this time, it is uncertain if these juice can be fermented into wine using just Brewer's Yeast, or if Nether Warts are necessary.
Kumis
Kumis is a form of fermented milk. At this time, it is unclear on how to ferment the milk - it could be as simple as pouring a bucket of milk into the Fermentation Barrel and adding Brewer's yeast, but a confirmation would be appreciated.