Yes, you don't have to install Leopard first.
Requirements for OS X 10.6 'Snow Leopard'
The OS 10.6 Snow Leopard install DVD is 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.
You should now see the App Store icon, and you now need to set up your account:
To use iCloud you have to upgrade at least to Lion, but some functions are only available in Mountain Lion:
You can also purchase the code to use to download Lion (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
Mind you, the most important thing before you do any upgrade is backup your data: https://discussions.apple.com/docs/DOC-1992
Upgrading to 10.6 these pitfalls may be met:
Upgrading to 10.7 these may be met:
Most important, all your PowerPC apps will become unusable, and need to be upgraded before upgrading to 10.7 or later. And upgrading to 10.8, these may be met: