No upgrade to the next version of OS X has ever been free.
Updates to the version you are already running are free.
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
OS 10.6 Snow Leopard is once again available for $19.99 from the Apple Store:
and in the UK:
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.