There are 3 main variables (a.k.a. "The 3 T's") which affect the quality of extraction: Time, Turbulence and Temperature.
Time refers to the brewing time, or the time that the water is in contact with the coffee grounds. Extractions occurs rapidly and slows down over time as the coffee mass and oils are removed from the grounds. Again, too little water contact with the beans will result in a diluted/weak coffee. Too much water contact will result in a burnt/bitter tasting coffee.
The time that the water should be in contact with the beans depends on brewing method. Pour-over and plunge presses should be around around 4 minutes while drippers should drip for between 2-3 minutes.
Another factor to consider is the time between brewing and consumption. Coffee is only fresh for about 10 - 15 minutes after brewing - there's just no substitute for a fresh cup of coffee! Try to brew just enough coffee that will be consumed right away. Aficionados would never reheat a cup of coffee but of course, there is no harm in doing so and it is certainly preferable to wasting it.
For manual brewing methods, you will need to experiment with the time the water is in contact with the beans and adjust your times accordingly. In general, it is recommended to keep the water in contact with the beans for between 3 and 4 minutes for pour-over / pressing methods. Pour the water slowly in concentric circles allowing the water to raise the slurry about halfway up the cone. Stir the slurry gently once (and only once) to ensure full saturation. Continue to pour the water and allow the bed to bubble and expand to maximum size. As it begins to subside about halfway down, add more water. The duration between expansions should be approximately 30-45 seconds. This technique is called "blooming the coffee" and will dramatically improve the extraction quality and overall "robustness" of the coffee.