You may want to start with Part 1
Xmonad is a tiling window manager. That means that, with very few exceptions, it lays out all of the windows in your workspace so that they completely fill the screen. You can have multiple layouts, and flip between them with a single keystroke. You can bring a workspace (there are 9 by default, but you can add more) to your screen with a single keystroke, or send a window to a workspace.
And the whole thing is configured using a text file that is actually a program, written in the functional language Haskell. I'll get to that later.
One of my main gripes about Gnome, etc., and one of the things I miss the most about CTWM, is that when you first start a program its window shows up at some random location on the screen, with whatever size the program thinks is appropriate. If you don't like those choices you have to move and resize the window yourself, and then do it all over the next time you log in. (There are some exceptions -- many newer programs remember where you put them last, and older programs, from the CTWM era, can be given a starting geometry.)
Xmonad's layouts are all deterministic, which is to say, predictable. When you start a program, you know exactly where it's going to be on the screen. When you change the layout, you know where everything is going to go. If you want to move a window into the main position (most layouts have one; e.g. the left-hand column) it's (as usual) just one keystroke to put it there.
But the best thing, and the reason I switched to xmonad in the first place, is the way it treats multiple monitors: it simply assigns one workspace to each monitor.
Undock your laptop, and its screen stays exactly the same. The workspaces that were shown on the other screens simply go back into hiding with all the others, and are still only a keystroke away. When you have multiple screens, you can move a window to another screen, or bring a workspace to a screen, or warp the pointer to another screen, all with single keystrokes.
When you go to a conference room and plug in a projector, a workspace immediately shows up there and its layout automatically adjusts to the projector's resolution and aspect ratio. When you get a new computer -- all the developers at work got new laptops just a month or two ago -- just copy your configuration files to it and everything will be exactly the same as it was on the old one. (Sometime later I'll write about my portable configuration, which makes it possible for me to set up my entire working environment in mere minutes.)
So let's go a little deeper into those magic keystrokes. First of all, you have to know that all of the commands (you can't really call them shortcuts) include a key that xmonad calls "Mod" (short for "modifier", of course). Mod is initially defined as Alt, but the first thing any Emacs user is going to do is redefine it as something else, usually the "logo" key. (That's the one on the left between Ctrl and Alt that usually has a Windows logo on it. If your keyboard has replaceable keys you may be able to get a penguin for it.) On old laptops that don't have a logo key I use Ctrl-Alt, but that's a matter of taste.
You also probably want to know that Mod-? gets you a list of all the commands. And that there's a fantastic collection of tutorials, documentation, and sample configuration files at xmonad.org.
When xmonad starts up, you see a totally empty, black screen. Most people, myself included, add a status/navigation bar at the top, but you don't have to. I'll get to that later. You can start a program by typing Mod-P, or open a terminal window with Mod-Shift-Enter. You will immediately notice that the first window you open fills the screen. If you open another, xmonad will tile the screen with them, showing them side by side.
If you start a third program, it will get added to the right-hand column. You can probably see where this is going. When you move the mouse pointer into a window, it gets a thin red border to show you that it has "focus".
If you decide that you started things in the wrong order, move the pointer into the window you want to put in the left-hand column (the "master" column) and hit Mod-Enter. You close a window you're done with using Mod-Shift-C.
Here's where it gets interesting: Mod-Space will switch you to a new layout, with the master column turning into a master row, and all the other windows across the bottom. Hit Mod-Space again, and the currently-focused window goes full-screen. (I reconfigure my full-screen layout to put a row of tabs across the top. Wondering how to see the hidden windows? Mod-Tab moves focus to the next window in the stack. It also works in other layouts, so you don't need the mouse to move focus around. If you spend most of your time in a terminal and an editor like vim or emacs, you can throw your mouse away and still be productive. Mod-Shift-Tab moves focus to the previous window.
Mod-2 puts you into a second workspace. There are nine of them. (I add two more -- 0 and -.) If you want to move a window, say from workspace 2 to workspace 1, use Mod-Shift-1. That's kind of a recurring theme in xmonad -- Mod-something does one thing, and Mod-Shift-something does something related.
You can see that in action if you add an(other) monitor. Now, workspace 1 is in the left-hand screen, and 2 is in the right-hand screen. Think of the two of them as West and East.
Now, Mod-w will move the focus (and the mouse pointer) into the West screen, and Mod-e will move the focus into the East screen. Mod-1 through Mod-9 will bring that workspace into whatever screen has the focus. If the other workspace was already visible, they trade places. (Some people don't like that, so you can change it so that it just moves focus into the other screen if you select a workspace that's already visible.)
Add a third screen to the right of East, and call it Right. Now, Mod-r and Mod-Shift-R do exactly what you would expect. (There are no bindings for T, so I suppose that if you have space for a fourth screen you could use it for that.)
There are more key bindings, to move focus (Mod-j and Mod-k focus the next and previous window, respectively; shifted, they swap the focused window with the next or previous window), to shrink and enlarge the master area (Mod-h and Mod-l respectively), or increase or decrease the number of windows in the master area (Mod-Comma and Mod-Period respectively).