The problem with Oracle is that its a huge product or in fact range of products. If your talking about the Oracle RDBMS then even with that your looking at something pretty big in terms of learning it. Just installing the think takes loads of experience.
If you do want to give it a go my advice would be if you don't already have it, install a copy of 8i and not 10g or 9i, the features offered by 9i and 10g are not really relevant for the beginner and there's plenty of scope in 8i for you to learn. Thats not to say that if you have any other version at work not to use them but the installation of 8i is relatively easy. Its avaliable for download for free from the Oracle website.
As for learning it free, well theres plenty of sites like this around where you can ask questions but as for a structured course I doubt you'll find one. Having said that Oracle offer all of their documentation on line. I'd say start with the Oracle concepts manual first and go from there. You can download them all from http://otn.oracle.com