How do I upgrade from Mac OS X 10.5.8 to the latest version on my imac 8.1?

Question

Here are my specs:
  Model Name: iMac
  Model Identifier: iMac8,1
  Processor Name: Intel Core 2 Duo
  Processor Speed: 2.8 GHz
  Number Of Processors: 1
  Total Number Of Cores: 2
  L2 Cache: 6 MB
  Memory: 2 GB
  Bus Speed: 1.07 GHz
I am trying to upgrade from Mac OS X 10.5.8 which is outdated to the latest version which is compatible on my computer? Does apple have an online adress for upgrading? I cannot pay for it right now.
Thank you

Answer 1

Upgrading to Snow Leopard
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mavericks if your computer meets the requirements.
     Snow Leopard General Requirements
       1. Mac computer with an Intel processor
       2. 1GB of memory
       3. 5GB of available disk space
       4. DVD drive for installation
       5. Some features require a compatible Internet service provider;
           fees may apply.
       6. Some features require Apple’s iCloud services; fees and
           terms apply.
Upgrading to Yosemite
You can upgrade to Yosemite from Lion or directly from Snow Leopard. Yosemite can be downloaded from the Mac App Store for FREE.
Upgrading to Yosemite
To upgrade to Yosemite you must have Snow Leopard 10.6.8 or Lion installed. Download Yosemite from the App Store. Sign in using your Apple ID. Yosemite is free. The file is quite large, over 5 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 Mavericks/Yosemite- System Requirements
      Macs that can be upgraded to OS X Yosemite
         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.