Roasting the Coffee Beans
- Light roasts are better for specialty coffee because there is less bitterness and it lets out the specific flavour of the beans.
- Dark roasts are more bitter as they are more roasted, but the acidity goes down.
- It is not ideal to roast coffee in an oven -- but there are ways to do that either in a pan (stirring the beans the entire time) or in a shakeable holed pot you shake around, making the beans tumble around the donut-shaped metal thing.
There are about two "cracking" moments when roasting, it is where the beans "crack"; when they reach a certain level of roasting.
Grinding
There's a whole section I wanna make about grinding cause the way it influences brewing and the funny and clever ways people have come up with solutions to that interests me too, but I haven't yet have had the time to
Technical Terms Coffee Nerds Use and Trends I've Seen
- Puck prepping: That intricate ritual where you prepare the coffee grounds into the portafilter before making an espresso in an espresso-making machine. It can involve many things such as the specifics of the grinding, poking and moving around the coffee grounds with needles to make them more even (WDT?), pressing them with a tamper to make water struggle more inside the portafilter, in order to extract more flavour
- Espresso: a coffee which is denser, and usually less in quantity than filtered coffee. Has crema (the lighter part on top). The standard in any italian bar or coffee shop. (If you just ask for a coffee, this is what you get). To achieve it, coffee needs to be extracted quickly and with high pressure, usually with an espresso machine, but there are some funky alternative ways to achieve that, more on that below
- Filtered Coffee: A 'family' of coffee brewing methods whose preparation require you to put coffee grounds into some kind of (usually paper, but there are funky trends such as ones made of ceramic, apparently??) filter, and to pour hot water on top. Gravity does the work: water will go through the coffee and then through the filter, filling your cup with coffee. V60 and Chemex are considered filtered. More "watery" but you usually you can make more of it.
As an italian, I am contractually obligated to put this one first. Objectively the best way to brew coffee forever ever trust me 100%. 
It is a practical way to brew coffee which involves pouring water inside this mechanism, letting it brew for around 3/4 minutes, then pushing down the grounds of the coffee and then pouring it to drink. It uses a metal filter. Usually there is a bit of coffee grounds still in the cup when poured. Very popular in English-speaking countries, I hear.
It is a one-piece glass brewer, with a "handle" of sorts made of wood, and a little leather tie. Coffee is brewed through larger and thicker filters, using more paper; the thick part rests on the channel which lets the air out, in order not to clug it. 
Arabic coffee is a family of coffees brewn either in dallahs (in pic) or, nowadays, just on stovetops, and then served for guests. When served cerimonially, it is courtesy to accept at least one cup from the host. Coffee grounds are boiled in the item of choice and then served very little at a time in small cups. Spices such as cardamom or cloves or saffron may be added in the boiling phase to taste, and it can be served with sweet things on the side.
I am NOT getting into the etymology debate here, but; this coffee is brewed with very very fine coffee, almost flour-texture, and spices such as cardamomo can be added in. The coffee is poured directly in the water you drink. You drink the whole thing. It is best not to let the coffee+water boil, but arrive just before it boils, then raise it above the flame. I've seen people do it by running the cezve/briki (the metal pot which contains the water+coffee mixure) upon very hot sand, in order to make the liquid boil and form a foam.
This plastic contraption allows you to brew coffee with pressure: you put a paper filter there, fill the tube up with water, and literally press the thing down, like a huge air syringe, and the air pressure you create pushes the water through the coffee with force, brewing it quickly. It's portable and fast, I'll give it that.
This one is funny. Looks and works almost like a Moka but you flip it meanwhile. Hey, instead of me telling you boringly how to do it, listen to 
The department's coffee machine broke and only delivered dirty water for an entire morning.