Coffee is one of my big splurges, and I'm still working on how to brew a better cup. I'll list some of the things I have learned, including some reiterations of the above points:
1. Good, fresh beans. I like a couple of local coffee shops that sell high-dollar coffee and roast their own. I'm talking about 3 to 5 times the cost of generic ground coffee in the supermarket. This one is well worth it to me. Also, if it sits around it loses its flavor.
2. Grind just before you brew. I use a blade grinder. I was using a burr grinder but it broke and I haven't taken the time to fix it yet. I really couldn't tell the difference. The main thing is to grind just before you make it.
3. Clean. Despite what everyone says, I keep my stuff surgically clean. I think it tastes better than leaving the skank residue folks seem to recommend.
4. Right Strength. This can make a huge difference. Strong vs. Weaker coffee are almost like different beverages. Try different concentrations... it brings out different flavors. I measure by volume. I usually try for somewhere between 6 water to 1 coffee up to 4 water to 1 coffee. My ex girlfriend used to go as strong as 2 water to 1 coffee, but that is not for the faint of heart! Keep in mind that a typical coffee maker uses 5 ounces as one cup instead of the standard 8 ounces, and that there are two tablespoons per ounce.
From there, I like to mix things up occasionally
I really like the "stovetop espresso makers" by Bialetti, among others. This makes some seriously good coffee! Buy the stainless steel model, in 6-cup or larger. Aluminum may be connected with Alzheimer's, so I avoid it in my food if possible. Use lower heat, just enough to boil the water. Too much heat makes it brew too fast.
I like a french press. When doing this:
1. Water temperature. I bring the water to a full, rolling boil, then remove from heat and let it cool for one minute (timed).
2. STIR!!! Stir the stuff for 3 or 4 minutes using a wooden stick or spoon... it makes ALL the difference.
3. Let it sit for another couple of minutes before you press and then serve immediately.
If you do the drip thing, try using two filters. This holds the water on the grounds longer and makes a much richer brew.
Mmmmm.... Coffee!
