You can activate action buttons by clicking on an icon or by pressing the key that is bound to it. The game default shows one row of action bars at the bottom of the screen. The left half of this action bar is bound to number keys 1-0 and then - and =. You can add more rows of action bars now or wait until later. You will definitely need a place to lay out your tasks as you get more and more options. I do it first thing when I make a new toon. If you go to your game menu by hitting escape or by clicking on the
little computer icon in the bottom right action bar, you will see an
option for interface. Click it and you get a screen with a menu on the left. Click the ActionBars menu and then select all of them. Do not check to make them visible, so that you won't even know they are there until you want to put an icon into them.
You can drag icons from your spell book to the action bar. You can rearrange them once they are there by holding shift and left-click as you drag the action to a new spot. You can play around with it, but most people move their main rotation of hits/spells to the 1-2-3-4 keys.
You can also bind actions not in your spell book. Go back to the Game Menu and select Keybindings this time. You will see so many options for binding keys it will be intimidating. Don't worry. Read through for future reference. You can put mount/dismount on a key once you can ride. You have target functions and chat functions. Play a while and then check back to see if there is a pre-programmed key-bindable action written for you to make your game play easier.
If you are going to bind to a letter key, however, scroll through the list to make sure you are not un-binding something important if you assign a letter to an action. One thing I like is to have a key to stop auto-attack. I put it on the C key, which by default is simply an action to sheath/unsheath your weapons. It doesn't do anything active in the game, and so I don't mind giving up the key for that.
Don't go crazy with this. You can keybind so many items you might have a hard time remembering them all, so you want your most common actions on the main action bar in the left hand number keys. That way you can press buttons to fight while moving around using the mouse with your other hand.
If you really start to jam up and have a hard time finding the right key for everything you want to do, you will have to start making macros, which are custom icons that you can write instructions for that combine and automate some stuff for you. More about that later.