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 appearsĀ  you will have to select your language and proceed to the next step.
OS X chooce your language

When Install Mac OS X appear, click “disk utillity” from upper menu
OS X  disk utility
Than choose your HDD, click on “Partition”, select one partition, name it the way u want and click on “Options”
OS X partitioning
Select “Guid Partition Table” and click OK
guid partition table
Now click Apply, and “Partition” and after a minute when it’s finished close “Disk Utillity”
os x partition table

os x partition
Now you are back to Install Mac OS X screen, click “Continue” and “Agree”
install mac os x

agree to terms

Than select “Customize” and deselect printer drivers to free up more space and click “OK”
customize mac os x install

deselect printer drivers

Now click on your HDD where You want OS X to install and press “Install”
HDD select
The installaton will now start, and it will last for about 20 min(depends on your comp. specs).
installing process

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