I have recently purchased an iPhone 4S and i am surprised to learn I cannot pair it to my Macbook Air via bluetooth. Actually, I have been unsuccessful in pairing the iphone 4S to any device via bluetooth. Kindly guide me in this regard.

Not & never has been a feature on any iPhone. Been this way since the first iPhone was introduced in 2007. File transfer, by bluetooth is not supported. These are the only supported bluetooth profiles:

http://support.apple.com/kb/HT3647

Pair it for what?

Syncing with iTunes is done via a USB connection with your computer, or syncing can be done via wi-fi when the computer and iPhone are connected to the same wi-fi network. Either one is much faster than syncing via bluetooth especially for music, movies, larger apps, and a number of photos. You can pair the iPhone via bluetooth with your computer for tethering but that is about it for bluetooth.

http://support.apple.com/kb/HT3647?viewlocale=en_US&locale=en_US

I'm trying to pair (bluetooth) my iPhone 4S with my MacBook Air for tethering but they are not pairing. The iPhone 4S can't "find" the MacBook Air. Both have bluetooth enabled and are very close (10 cm) one to the other. Should that work?

The Apple article below should get you going.

http://support.apple.com/kb/HT4517