Q: how do I upgrade my imac snow leopard 10.6.8

That would depend on the make and model of your Mac. Go to the Apple Logo, top eft of your screen > About This Mac and post the hardware and model details of your Mac.

Cheers

Pete

Your basic options are:

Upgrading to Mountain Lion

To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase a redemption code at the Online Apple Store: OS X Mountain Lion. Mountain Lion is $19.99 plus tax. Use the code to redeem a download of Mountain Lion from the App Store. 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) - Model Identifier 7,1 or later.

         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model

             Identifier 5,1 or later.

         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later.

         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later.

         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later.

         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later.

         7. Xserve (Early 2009) - Model Identifier 3,1 or later.

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

     Are my applications compatible?

         See App Compatibility Table - RoaringApps.

Upgrading to Lion

If your computer does not meet the requirements to install Mavericks, it may still meet the requirements to install Lion.

You can purchase Lion at the Online Apple Store. 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.

Or upgrading to El Capitan.

Yes. I would suggest you install more RAM if possible. The more the merrier.

Hi Kappy,

Quick one - how do I purchase Snow leopard to be downloaded directly to my iMac?

Snow Leopard is not available as a download. It will need to be purchased as shown below.

http://www.apple.com/shop/product/MC573Z/A/mac-os-x-106-snow-leopard

Thanks! Speedy response!  But I do not want it shipped! Any other way to purchase it for download?

As stated, it is not available as a download.

Yea, thanks...my eyes were trying to better your speedy response;)! Another question just to verify: from 10.5.8, the next upgrade would be Snow Leopard?

Yes, Snow Leoprad (10.6) would be the next step, and would be required for any further upgrades. The Snow Leopard link in my post has details for requirements. Kappy's post above has info for further upgrades.