You must have a Snow Leopard DVD to start. Is that what you have? If so then follow these steps:
Booting From An OS X Installer Disc
1. Insert OS X Installer Disc into the optical drive.
2. Restart the computer.
3. Immediately after the chime press and hold down the "C" key.
4. Release the key when the spinning gear below the dark gray Apple logo
appears.
5. Wait for installer to finish loading.
Erase and Install
1. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu.
2. After DU loads select your hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Note the SMART status of the drive in DU's status area. If it does not say "Verified" then the drive is failing or has failed and will need replacing. SMART info will not be reported on external drives. Otherwise, click on the Partition tab in the DU main window.
3. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Partition button and wait until the process has completed.
4. After formatting is complete quit DU and return to the installer. Complete the Snow Leopard installation.
5. Once Snow Leopard is running you must download and install Mac OS X 10.6.8 Update Combo v1.1.
6. You may now access the App Store in order to purchase and download Mountain Lion.
Upgrading to Mountain Lion
To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase and download Mountain Lion from the App Store. Sign in using your Apple ID. Mountain Lion is $19.99 plus tax. The file is quite large, over 4 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
OS X Mountain Lion - System Requirements
Macs that can be upgraded to OS X Mountain Lion
1. iMac (Mid 2007 or newer)
2. MacBook (Late 2008 Aluminum, or Early 2009 or newer)
3. MacBook Pro (Mid/Late 2007 or newer)
4. MacBook Air (Late 2008 or newer)
5. Mac mini (Early 2009 or newer)
6. Mac Pro (Early 2008 or newer)
7. Xserve (Early 2009)
Are my applications compatible?
See App Compatibility Table - RoaringApps - App compatibility and feature support for OS X & iOS.
If the computer is not qualified to run Mountain Lion, then you can upgrade to Lion:
Upgrading to Lion
If your computer does not meet the requirements to install Mountain Lion, it may still meet the requirements to install Lion.
You can purchase Lion by contacting Customer Service: Contacting Apple for support and service - this includes international calling numbers. The cost is $19.99 (as it was before) plus tax. It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.
Lion System Requirements
1. Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7,
or Xeon processor
2. 2GB of memory
3. OS X v10.6.6 or later (v10.6.8 recommended)
4. 7GB of available space
5. Some features require an Apple ID; terms apply.