Switch Axe is my weapon of choice, and it takes a bit of learning but it can be quite effective. The X attack is good for hitting a tail that's over your head, Forward + X attack has amazing range and is great underwater, A+X is good when you're under a monster, and if you have the time to do so, after performing the A+X attack you can mash A to do a figure-8 swing that hits repeatedly (be careful as each swing drains your stamina so you may find yourself unable to dodge when this ends.)
In addition you have your sword mode, which can be accessed in 3 ways: Hit R while your Axe is out to switch, hit R after a Forward+X attack to switch and slash in one fluid motion, or while your weapon is sheathed, hit R+A+X to unsheath and slash in sword mode.
Sword mode is much shorter in range but is capable of some fluid strikes and a powerful discharge (A+X, then mash X until the tip of your sword explodes. Use this when the monster is knocked over or otherwise motionless.) Note that one of its attacks (Rising Slash in sword mode) is only accessible by using your secondary special attack button since R morphs the weapon. This is Start on Wii U or the touchscreen button on 3DS (Kick while sheathed, yellow sparkles with your weapon out.)
Really just stick with it and see how each attack works and you'll eventually begin to fully grasp how versatile Switch Axe can be with experience. I find that it's a nice balance between the brute force of Greatsword and the elegance of Longsword.
Thanks for the tips!