I would agree with many of the suggestions - I would break into two categories though..... The first two things, if not correct, will ruin your beer or result it bad beer. The other things are more about improving on already decent beer.
* Water/pH - Depending on your water supply/style you are brewing, I actually think this could be the #1 thing. If you happen to have a good water supply for the particular style you brew, it may make no difference. But, if you have water that is not good for brewing, it can ruin every beer you make. So, learning about your water is a key 1st step.
* Sanitation - Bad process = Bad Beer
Once you have those two down - these are some of the next ones that can improve what you are doing:
Yeast management, All Grain, quality ingredients, Temp. Control, oxygen control, etc. are all good suggestions that can take "good/average" beer to outstanding/great beer
***One thing that I would add, which made a HUGE difference for me is repetition. Pick a particular style/beer you like and brew it over, and over and over. Tweak one thing at a time to really get a feel for what you are doing, what impact your changes make, and really helps you understand brewing. Change things like water chemistry or yeast or grain bill, or hops, or process (low oxygen or other strategies). Isolate one variable each time and just brew that beer 10-20-30 times until you perfect it..... then move on to another style. Obviously, start with something you and your friends like to drink because you will kind of always have it on hand. Start with things that are simple, easy to brew, fast to turn around and make it a "house beer."
Some of the ones I have brewed 30+ times over the years, tweaking a little here and there and trying to "perfect":
Blonde Ale
NE Pale Ale
British Dark Mild
Dortmunder Export
German Pilsner
"Americanized" German Pilsner
Porter
Simple, classic styles are the types of beers you want to target for this type of thing. Learn to perfect a style (or several).... keep brewing "one-off's", but always have a certain style you are brewing over, and over, and over as you learn about it until you are satisfied with it and feel you can brew it great, in your sleep.