I have OS X 10.5.8 and want to update my OS. WHat do I need to do?

Question

What is the next step to getting toward Maverick?

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 Mountain Lion 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 from Snow Leopard to Lion or Mavericks
To upgrade to Mavericks you must have Snow Leopard 10.6.8, Lion, or Mountain Lion installed. Purchase and download Mavericks (Free) from the App Store. Sign in using your Apple ID. 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- System Requirements
       Macs that can be upgraded to OS X Mavericks
         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 by contacting Customer Service: Contacting Apple for support and service - this includes international calling numbers. 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.