My Mac is OS X 10.5.8, how to update??

You need to buy a Mac OS X 10.6 DVD; Mac OS X 10.6 requires an Intel Mac with at least 1GB of RAM.

(88759)

First you must purchase Lion, Mac OS X 10.6, from the Apple on-line store for $20 and install. Update that on-line download to 10.6.8. If you have at least an Intel Core 2 Duo processor and 2 GB ram and 7 GB free hard drive space you can then purchase the Lion download by calling 1-800-MY-APPLE and pay the $20 fee to get an email sent to you with the access code and process to download.

I think Ralph is having a 'senior moment'! 😉

OS 10.6 is Snow Leopard.

Start by checking if you can run Snow Leopard:

Requirements for OS X 10.6 'Snow Leopard'

http://support.apple.com/kb/SP575

The OS 10.6 Snow Leopard install DVD is available for $19.99 from the Apple Store:

http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard

and in the UK:

http://store.apple.com/uk/product/MC573/mac-os-x-106-snow-leopard

but nobody knows for how long it will be available.

When you have installed it, run Software Update to download and install the latest updates for Snow Leopard to bring it up to 10.6.8, or download the combo update from here:

http://support.apple.com/kb/DL1399

Check via Software Update whether further updates are required.

You should now see the App Store icon in iTunes, and you now need to set up your account:

http://support.apple.com/kb/HT4479

To use iCloud you have to upgrade at least to Lion, but some functions are only available in Mountain Lion:

http://support.apple.com/kb/HT4759

You can also purchase the code to use to download Lion (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:

http://www.apple.com/osx/specs/

It's always safest to have a backup or clone, but in theory, it should not destroy your files, just install new OSX & Apple Apps like Mail, Safari, etc.