I am pretty new to DSLR, and there is one thing I am curious about. I watched some videos and heard from my friends that it is ok to turn the power button on even you do not use the DSLR (camera will automatically turn off that power like computer). I am wondering if this is true and will it increase the speed of damaging the CMOS and other electronic components in DLSR?
I take it you mean leaving the switch always on, and letting the camera go to sleep after a timeout (as most cameras do).
This isn't going to hurt your camera in any meaningful way. It just wastes a small amount of battery. And if you store it that way, a bump of the shutter button could take some dark shots of the inside of your camera bag. Those things aren't normally desirable, so I generally turn mine off.
On the other hand, if you just leave it in "sleep" mode, the camera is faster to use — it usually takes less time to come out of sleep than to power on (although thankfully by now the time is negligible for most cameras in either case), and of course, that's one less switch to flip.
Most cameras I'm aware of retain all of their settings when going into sleep; different ones reset various things on full power-off. On some cameras (like those from Pentax), you can configure what you want to keep and what you want to reset, so your camera always starts in a known state, but that can be annoying if you're working in a certain situation where you want, for example, white balance to stay as you've set it, so you can "solve" that by not powering down for as long as you want those special settings.
It's also worth mentioning that automatic sensor dust removal usually happens at power on, shutdown, or both. If you decide to never power down manually, you may want to add the habit of running this by hand occasionally.