Below is a list of some brewing methods, in order of necessary grind type, from coarsest to finest:
Cold brew coffee is brewed with an extra-coarse grind and without heat (go figure!). It is usually steeped, much like you would brew tea. Cold brew coffee is generally less acidic and about 30% lower in caffeine, meaning it's a good option for those with acid reflux or a low caffeine threshold. It is also excellent for making iced coffee, because it won't get as watered down when you put ice in it, since it won't need to cool down from hot. It also requires no electricity!If you'd like to get started with cold brew, check out this affordable cold brew kit from Toddy
French Press is one of the most popular forms of "fancier" brewing methods that people use at home. It's easy to use, and produces a rich and delicious cup of coffee. To use it, you let coarsely ground coffee steep in hot water for 3-4 minutes before slowly pressing down the filter and serving. There are tons of different ways to brew it using different weights of coffee, volumes of water, water temperature, etc.
For an in-depth tutorial for how to use a French Press, check out this guide from I Need Coffee.
If you'd like to buy a French Press, check out this affordable option from Bodum
Despite the mad-scientist sounding name, the Chemex is a popular and fairly simple method of brewing. It consists of an hourglass shaped pot, where a filter is used to hold coffee while hot water is manually poured over the top. This method is all about pour technique and water temperature, and there are several other variables that can be changed as well, including grind size, although medium-coarse is the standard.
If you'd like to buy a Chemex for yourself, you can get the official Chemex branded one here.
Usually for a Chemex, water is poured using a gooseneck kettle, which you can purchase here.
Ah, the old standby. This is the type of coffee most people are familiar with. Whether you use a $15 college-dorm-sized coffee machine, or a high end fancy machine, it's all the same idea - heat up water, and drip it through ground coffee that sits in a filter. This method is the easiest way to brew coffee, because you don't have to do anything! Just press the button and wait. You give up some control in doing so, but if you're just trying to make a quick morning cup, this is perfect for you.
There are tons of different drip pot options out there, but here are three that I like at three different price points: