What are the most commonly used data backup methods for Mac OS X Yosemite version? Please tell me in detail about that. I need some reliable solution for my Mac OS X.
The most common solution by far would be Time Machine, which comes included with Mac OS X. Just by an external drive of (say) twice the size of your Mac's drive, plug it in, and Mac OS X will probably just ask if you want to start using it for Time Machine automatically.

If you're smart, you'll buy two drives, set them both up as Time Machine backups, and then rotate them between backing up your system, and being stored elsewhere.