Oops. Somehow I deleted my previous post.
Okay, I'm using FlashDevelop, though it should be similar for whatever environment you're working in (I hope...). Within FlashDevelop (or what have you), create a new AS3 Project named HelloFlixel. Then copy the com folder (containing the subdirectory adamatomic/flixel) from the flixel_v1.0 download into your project folder.
Your first actionscript file, HelloFlixel.as, should look something like this:
package {
import com.adamatomic.flixel.*;
public class HelloFlixel extends FlxGame {
public function HelloFlixel():void {
super(320, 240, HelloState, 2, 0xff000000, 0xffffffff);
}
}
}
I went ahead and imported the entire flixel library for simplicity's sake. All the games you make with Flixel must extend FlxGame. The FlxGame constructor as we're using it above takes arguments for width and height of your game, the FlxState to initiate, the zoom factor, the background color, and the flixel logo color (on startup). Here it's just white on black, but feel free to change the colors (the color format is 0xaarrggbb).
Now we need to create HelloState. Create a new file, HelloState.as, and make it look something like this:
package {
import com.adamatomic.flixel.*;
public class HelloState extends FlxState {
private var text:FlxText;
public function HelloState():void {
text = new FlxText(0, 0, 100, 10, "hello",0xffffffff);
this.add(text);
}
override public function update():void {
super.update();
}
}
}
Here we have HelloState which is an FlxState. We have a FlxText object named text, which we'll use to write some text to the screen. Within the HelloState constructor, we'll initiate our text. FlxText's constructor arguments here are x and y position, width, height, the String to write to the screen, and the color. (Additional arguments include font size, font face, etc. please feel free to look it up in the documentation). Then we need to put text into the update loop, by using this.add(text);. The update() function is called every frame; here we override it because it's already defined inside FlxState. We don't have anything special we want to do here yet (later you may want to add some interactivity or animation to this; this is where you would check for keypresses and the like), so we just call super.update(); and we're done.
From here you should be able to compile and run, and you get "hello" in the upper-left corner:

I know I left a lot of things out of this, and I don't really know what I'm doing. I'd appreciate it if anybody corrected me where I'm wrong, but also please feel free to ask questions; I'll try to answer.

I hope this helped somewhat.