Properties of the 360:
The 360 is made up of 3 clear spheres (inner, middle and outer), each with different properties:
The outer sphere has 6 colored domes and two black knobs. It is divided into two hemispheres, and each hemisphere has three holes that lead to one of the domes. The hemispheres are known as:-ROY: Red Orange and Yellow domes.
-BUUG: Blue, White, and Green domes.
The middle sphere has a horizontal axis (connected to the black knobs), a counterweight, and has two holes, each leading to one of the hemispheres.
The inner sphere has diagonal axis (connected to the middle sphere), a counterweight and one hole leading to the middle sphere.
The holes in the inner and middle layer are always open, but the holes in the hemispheres have gateways controlled by the black knobs that can be turned to cover up or allow passage through the holes.
The goal of the puzzle is to move the 6 colored balls from the inner sphere to their corresponding dome. You can accomplish this by shaking the 360 until a ball falls through the holes and into the outer sphere, and then use the knobs to move it into its dome. This method, however, is time consuming and is doubtful to impress your friends.
Another way to solve the puzzle is to control the spheres by using physics, involves absolutely no shaking, and can have you solving the cube in ~6 minutes and even faster with a little practice.
If you study the 360 you’ll see that the inner and middle spheres each have a counterweight and holes are positioned opposite the counterweight. The counterweights are pulled downward by gravity, and therefore gravity keeps the holes pointed up.
The trick to solving the 360 is to figure out a way to defy gravity and invert the spheres so that the counterweight is at the top of the sphere and the holes at the bottom. That way, the balls can fall through the holes and into the correct dome. Your 360 should come with "instructions" that say as much. With enough experimentation, you should be able to figure out how to solve without resorting to the Shaky-Shaky solution. But, if your stuck, I've organized the solution into 6 steps, presented in a way that allows either self discovery or allows you to jump ahead via hints and a spoiler solution.
Or, if you are a more visual learner: Here is a video detailing how to solve the 360 (Warning: it's a spoilers solution. If you just want some hints to figure out how to solve the 360 on your own- and trust me you are smart enough, it's not rocket science- use the links above.)