Q: update from a Mac os x 10.5.8 to a 10.6

It seems you already have the latest version.  If you want the latest update you can either use the software update in the system preferences or Google for the combo update, which includes everything from first to the last version:

http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update

10.6 is Snow Leopard.  If you want that you have to buy a retail disk, which you can probably get on ebay for five bucks.  In my opinion this is a much better option than going to 10.7 or 10.8, which are available on the Apple web site.  I am sure others would disagree with me and say 10.8 is better but you might need to buy new software.  Indeed, you might have to keep this in mind if you go up to 10.6.  I think I had to buy a new version of Photoshop, which stopped working when I upgrated to 10.6.

Correction;

10.6 from eBay or Amazon is going to set you back from $50 to $the _skies_the_limit.

Snow Leopard DVD

You can get it only by phone now from Apple.

In the US, call 1-800-MY-APPLE and ask for a sales assistant. Last quoted price was $19.99 for the single-user and $29.99 for the family licence.

For other countries, check here; http://support.apple.com/kb/HE57

Don't forget to ask for Sales; the tech support guys can't help.

If you are contemplating buying from elsewhere, be aware that the only disc that will work is the retail SL disc, which is 10.6.3 and is white with a pic of a snow leopard on it (now there's a surprise!);

Grey discs may well be available cheaper, but will not boot or install on your Mac.