You will have to set up an environment containing at least of the SAP Netweaver Developer Studio (a customized Eclipse 3.3) and the SAP NetWeaver Application Server. As oozoo already mentioned, there is a trial version containing both components.
With this trial version you can try some tutorials from the SAP Developer Network. The following page is a good starting point:
http://wiki.sdn.sap.com/wiki/display/WDJava/Welcome+to+Web+Dynpro+Java!
For developing in Web Dynpro it is not mandatory to know about SAP ERP systems. In my company for example, we use it to build GUIs for various preexisting Oracle DBs. But I agree that Web Dynpro differs a lot from most other Java Web Frameworks. It has a very unique component model that takes some time to get used to.
What's also quite special is that you don't code any HTML or JavaScript by hand. You only use the many GUI components provided by Web Dynpro. It is comparable to GWT in that respect. Only in the most recent version you can use so called WebWidgets in to include some custom HTML for special use cases.
Usually Web Dynpro is used in combination with the NetWeaver Development Infrastructure (NWDI) which consists amongst others of a proprietary source control system (Design Time Repository - DTR), a software lifecycle mangagement tool (Change Management Service - CMS) and a continous integration server (Component Build Service - CBS).