how do I update my Mac OS X Snow Leopard 10.5.6 for Mac OS X 10.6 Snow Leopard

Purchase and install Snow Leopard.

Minimum requirements here > http://support.apple.com/kb/SP575

You can purchase SL from the online store > http://store.apple.com/us/product/MC573Z/A?mco=MTY3ODQ5OTY

If you are considering upgrading to Lion after Snow Leopard, make sure your Mac meets Lion's requirements:

Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM

You presently have Leopard installed. You will need to purchase a retail copy of Snow Leopard at any Apple store or Online Store - $29.00.

Snow Leopard General requirements

• Mac computer with an Intel processor
• 1GB of memory
• 5GB of available disk space
• DVD drive for installation
• Some features require a compatible Internet service provider; fees may apply.
• Some features require Apple’s MobileMe service; fees and terms apply.

How to Install OS X Updates Successfully

A. Repair the Hard Drive and Permissions:

Boot from your current OS X Installer disc. After the installer loads select your language and click on the Continue button. Then select Disk Utility from the Installer menu (Utilities menu for Tiger and later.) After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.

If DU reports errors it cannot fix, then you will need Disk Warrior (4.0 for Tiger) and/or TechTool Pro (4.5.2 for Tiger) to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.

B. Make a Bootable Backup Using Restore Option of Disk Utility:

1. Open Disk Utility from the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Check the box labeled Erase destination.
5. Select the destination volume from the left side list and drag it to the Destination entry field.
6. Select the source volume from the left side list and drag it to the Source entry field.
7. Double-check you got it right, then click on the Restore button.

Destination means the external backup drive. Source means the internal startup drive.

C. Important: Please read before installing:

1. If you have a FireWire hard drive connected, disconnect it before installing the update unless you will boot from this drive and install the update on it. Reconnect it and turn it back on after installation is complete and you've restarted.
2. You may experience unexpected results if you have installed third-party system software modifications, or if you have modified the operating system through other means. (This does not apply to normal application software installation.)
3. The installation process should not be interrupted. If a power outage or other interruption occurs during installation, use the standalone installer (see below) from Apple Downloads to update. While the installation is in progress do not use the computer.

D. Download and install update(s) if updating:

1. Use Software Update, or
2. Download standalone updater(s).

E. To upgrade from an earlier major version:

1. Purchase the requisite installer package (Snow Leopard for example.)
2. Boot from the installer DVD.
3. Choose the install option: