This tutorial shows default Mac OS X Snow Leopard installation, everything is more less the same for Lion and Mountain Lion, just a slightly different changes in a design.
This is basic and default way to install OS X on Mackintosh machines (installing boot loader and after install procedures are not included cause this is only needed for Hackintosh computers)

So, first boot your copy of a retail DVD, or USB installation media with OS X on it.
When installation screen appears  you will have to select your language and proceed to the next step.


When Install Mac OS X appear, click “disk utillity” from upper menu

Than choose your HDD, click on “Partition”, select one partition, name it the way u want and click on “Options”

Select “Guid Partition Table” and click OK

Now click Apply, and “Partition” and after a minute when it’s finished close “Disk Utillity”

Now you are back to Install Mac OS X screen, click “Continue” and “Agree”

Than select “Customize” and deselect printer drivers to free up more space and click “OK”

Now click on your HDD where You want OS X to install and press “Install”

The installaton will now start, and it will last for about 20 min(depends on your comp. specs).

And finally, if everything went ok, you are finished with install succeeded message