Note: This guide is not intended to be a comprehensive, end-all / be-all resource for keybinding techniques and strategies- these guides already exist elsewhere on the interwebz, and have been written by much more proficient players than myself. This guide is only intended as a starting point, a basic, general overview of keybinding for players new to the practice.
-- What Is Keybinding? --
To begin, let's start with the most basic question: "What the heck is keybinding, anyway?"
Keybinding is the practice of assigning (via the Blizzard Interface menu or via an add-on such as Dominos) various abilities placed on a player's action bar to a specific, unique key on the keyboard or mouse (if applicable), or to a unique combination of keys. Basically, whenever the player hits the key (or key combination) to which an ability is bound, that ability is then used (macros, also, are bound in this manner - for more information on macros, Raygecow has an excellent guide for beginners:
The short version: you hit a button, you do something. Bam. Simple. Moving on.
-- The Virtues of Keybinding --
The next question that comes up is, "Why should I keybind?"
Without going into too much mind-numbing detail regarding the differences in dungeon, PvP, and raid performance from those who keybind to those who don't, the bottom line is that players who keybind have a much faster response time to what is happening around them, able to unleash a string of abilities in the time in can often take a "clicker" (someone who doesn't keybind) to find just that one spell. Keybinding transfers an ability rotation from a player's visual memory to a player's muscle memory, allowing him or her to react sometimes before they're even aware of what they're reacting to.
The short version: keybinding saves time and effort. Why not make the game easier for yourself?
-- Binding Keys and Keybinding Logic --
Now we come to the good part: "How do I keybind?"
Back in the day, we had to do this thing called "manual keybinding," which meant that we had to go into the Blizzard Interface menu and manually change and re-arrange our keyboard layout to suit our rotation and style of play, one key and key combination at a time.
This meant that you had to know how each Action Bar was laid out in order to bind your keys (Bar 1, Button 1; Bar 3, Button 5) etc. This could often take a great deal of time to steamline and set up effectively (and those of you who want to learn how to do this can simply go into the Keybinding menu and play around with it to see what I'm talking about: Esc --> Key Bindings).
More recently, we've taken to using (and recommending the use of) add-ons like Bartender and Dominos for this task- Dominos, especially, is a major time-saver due to the fact that it lets a player mouse-over the Action Bar slot they wish to bind and simply hit the key or key combination they wish to bind it to. Bartender does offer some further customization over Dominos, but Dominos is much more user friendly and what I recommend for those new to add-ons / keybinding.
The following sections can easily be put into practice using either medium mentioned above.