Methods of Brewing Coffee
There are numerous methods for brewing coffee, each with its own unique process and resulting flavor profile. Here’s an incomplete list of various coffee brewing methods:

Pour Over
Drip Brewing
French Press
Espresso
Cold Brew
AeroPress
Siphon/Vacuum
Turkish Coffee
Moka Pot/Stovetop Espresso
Percolator
Chemex
Clever Dripper
Soft Brew
Vietnamese Phin
Nel Drip
Coffee Bag
Instant Coffee

As for the most popular methods, it often depends on personal preference, cultural factors, and the desired outcome in terms of taste and convenience. However, some of the most popular methods include:

Pour Over: This method is favored by coffee purist for its ability to highlight the coffee’s flavor nuances and produce a clean cup. It involves pouring hot water slowly using a thin necked kettle, over the coffee grounds in a filter, allowing the water to drip through into a carafe or mug, then letting the coffee breath for two to three minutes. 

Drip Brewing: This method used by automated coffee machines is also favored for its ability to highlight the coffee’s flavor nuances and produce a clean cup. 

Espresso: Known for its strong flavor and concentrated form, espresso is made by forcing a small amount of nearly boiling water through finely-ground coffee beans. It’s the base for many other coffee drinks like lattes and cappuccinos.

French Press: This method allows for full immersion of the coffee grounds in hot water, resulting in a rich and full-bodied cup. It’s appreciated for its simplicity and the depth of flavor it can extract.

Cold Brew: Gaining popularity for its smooth, mellow flavor and low acidity, cold brew coffee is made by steeping coarsely ground coffee in cold water for an extended period, usually 12 hours or more.

How to taste coffee for flavor
First make sure the coffee is not to hot or your tongue will burn. Next take a sip with no cream or sugar and swirl the coffee around your mouth and the bottom of your tongue. You should be able to taste all the flavors that make up freshly roasted and ground coffee beans.

Brewing Method Effects Taste
Each of these methods has its own set of enthusiasts and is popular for different reasons, such as the ease of use, the ability to control brewing variables, the texture of the coffee, and the distinct flavors that can be achieved. The choice of method can also depend on the time available for brewing and the equipment at hand. For example, espresso requires a specialized machine, while pour-over can be done with just a cone and filter.

Ultimately, the best method is the one that suits your taste preferences and lifestyle.