[while in the midst of typing ElPugDiablo put an excellent post! ... What he said]
Short answer:
If you use fresh roasted beans, good burr grinder--properly adjusted, grind to order, with proper brewing techniques you will put yourself in the top 10% easily.
Semi-detailed
Quality, Freshness, Machinery, Proper Technique
I think you have to have quality coffee, fresh, properly brewed to know what it should taste like. The coffee is where you don't skimp. Expect to pay avg. of $3.00++ per pound if you roast your own, and $8+ wholesale from a quality roaster. Beware of anyone hocking $5.00 roasted coffee, it will not be good.
1) Go to a "known" quality shop (look to Coffeegeek or the BGA boards for recommendations) and try different origins, brewing methods, etc. of coffee OR
1a) Order fresh coffee from a known quality shop and brew at home to test.
2) After that it's pretty simple.
A) Quality of beans (No generic beans. -- (ok)Guatemala vs. (better)Guatemala Huehuetenango vs. (best)Guatemala Finca El Injerto)
B) Freshness -- order fresh, maybe once a week or every ten days. Throw out anything that hits three weeks from roast date. If your truly quality oriented 7-10 days post roast.
C) Clean, well-maintained adjustable burr grinder.
D) Correct coffee to water ratio, brewing temperatures, time, and methodology for all brewing methods you may use.
"D" is an entire book on its own, but suffice to say, make healthy use of the "search" function on every coffee board you can, along with a good dose of reading, watching, visiting shops.
The fact that you are exploring this will put you ahead of many. Happy caffeinating!