You may have noticed that you only have a few spaces to equip skills on your pet bar, but you will learn a whole lot of skills with the new pet talent trees. At first I thought this meant I could only use so many skills at once, but this isn't actually true. You can use all the skills you have learned at the same time. You just need to do some macro work.
First of all, you don't necessarily need to use this method as many skills can be set to automatically be used whenever possible. If you open your spellbook and right-click the skills, it will toggle a glowing outline on and off. When the skill is glowing, it will automatically fire each time your pet has a chance to use it. If it's off, you will have to manually use the skill each time you want it used. Because sometimes you just don't have enough fury to go around, I will teach you how to manually set skills to your action bar.
First open the system menu and go to macros. Create a new macro and set its name and symbol to something related to the skill. Then simply type "/cast NameofSkill" into the macro box. Just make sure the name of the skill is typed correctly and there is one space between the /cast and the skill name. Then drag the macro into your action bar and you're good to go. It's really that simple.