You can either use the Recovery partition (if it's still functional - holding down the Command and R keys whilst booting) or use straight Internet recovery (holding down the Command, option/alt and R keys whilst booting).
You can also redownload the Mountain Lion OS and quit before it begins installation. There will be a file in your Applications folder named "Install OS X Mountain Lion.app". If you have this in your Applications folder, you can use Lion DiskMaker to create bootable media (a USB thumb drive or a dual-layer DVD) that can also serve in case of an emergency.
Personally, I have an entire system with the ML installation and variety of utilities on a 64GB USB drive. Slow to boot but can work well with my Mac just in case everything fails at once (unlikely since I keep redundant backups of everything).
1- Why it asks for internet in the instructions? Isn't it suppoed to install from a hidden recovery partition?
Because it downloads the OS from Apple's servers...the hidden recovery partition does not contain the OS itself. You can make your own recovery boot disk...use a USB thumb drive...obviously much quicker.
2- And how you can verify that your Mac has one and is functioning?
Re-boot while holding down Command + R.
3- If you have Windows via Bootcamp, does doing this recovery, affect Windows?
Best thing to do is keep two backups, one being Time Machine, & the other a bootable clone. Do that, & you will be back up & running in minutes if something goes wrong.
1. If you refer to Recovery HD, it hasn't got Mountain Lion on that volume. It downloads OS X from the App Store.
2. With bootable clone, we refer to use a program like Carbon Copy Cloner to make a bootable clone of your hard drive on an external disk so, if you can't start from the hard drive, you can connect the external disk and use your Mac. It's useful also after replacing the hard drive because you don't have to reinstall Mac OS X
Have you read this?
If you want to create a bootable thumb drive for your Mac, follow the instructions on this website extract:
This works because I have tried it successfully.
Message was edited by: OGELTHORPE