By the way, do i have to have an internet connection to install operating system on mac?
No, you don't need the internet for installation.

If it's just a dmg, it's not bootable. Sorry, mate!
You'll need another disc. The dmg can be used for upgrades only. You cannot boot from it.
If a buy a bootable cd and insert it, will it show in disk utility? Or in the place where i should start the setup?
You don't buy a bootable CD, you make one. A bootbable disc is just a disc with a certain structure that allows booting from.

Here's the thing now. Usually, if you burn an OS dmg from a Mac, it's automatically turned into a bootable disc. But with Mountain Lion, it doesn't seem to work.

You need to download a bootable iso. Happened to try this a couple of days ago.
I am in disk utility now and i can see mac drive and super drive (dvd) and another one lower of those two named mac os x base system.
I choose the macintosh hd as the destination. Should i choose the mac os x base system as source and press restore?
What are you doing now?
I choose the os-x.dmg as source and macintosh hd as destination and iam restoring.
Restore failed after 16 minutes
Error 206
Why when i boot and press options the only drive displayed is the recovery partition?
As i can see that the macintosh hd should also appear!
Issue resolved. For future reference:

I inserted a usb flash and booted into recovery mode,formatted the usb using disk utility.
I restored the image file from the dvd i already have to the usb. I had an error message when done rewtoring but i restarted and went with the installation process. All went fine, i have now the mountain lion installed