If you want to get experience with the Salesforce without taking expensive classes then, first of all I have a question if I am on your side is that what exactly I want to accomplish, because in salesforce there are many works for example Configuration focused admin work or developing applications on the platform, generally involves some development work.
Or, another way, a great starting point is, as stated, create a developer account. In addition to that, however, a great way to step up your initial admin understanding is to check out a number of the free videos salesforce has on their podcast: Administrators Sessions - Dreamforce 2011.
After learning and familiar with the above sessions, I would practice configurations in the following situations:
- Creating new, inter-related objects
- Creating new custom fields
- Dealing with formulas and validation rules
- Spend a lot of time in workflow rules
- Approval Processes
After following and learning as admin side, the best tools for the development side is via some of the ISV documentation salesforce has, and some of their Apex and Visualforce exercises.
The main thing is to learn here are around governor limits and packaging, this is because if you want to look to build apps for Salesforce, so it will save your headache in the future.