Verified answer

There are no just simple algorithms to solve it. There are methods. The fastest methods are F2L keyhole method, and the Fridrich method.

About your cube, if it's falling apart when you turn it quickly, it's either because you lubricated it with Vaseline or petroleum jelly or any oil based product, or it's just a cheap cube.

DO NOT lubricate your cube with Vaseline or petroleum jelly or any oil based product. They eat up the plastic inside your cube, so even if it makes it super smooth, it will lock up and pop alot because there will be less plastic to support the inside of the cube. If you want to lubricated the cube, I recommend silicone spray.

If you want to learn how to solve the Rubik's cube, try one of these websites for solutions. I find them pretty easy to understand:

http://www.learn2cube.com/

http://peter.stillhq.com/jasmine/rubikscubesolutio...

If your screws have removable center caps, you could tighten the screws. Otherwise I would suggest getting a new cube.

Hope this helps! ;D