Our system operates under the principle that data owners are the sole and final arbiter of access to their data. The Enterprise GIS team itself maintains certain "basemap" data layers, but as a new user of the system, you will need to negotiate access to more specific data layers managed by other users.
We are developing a web-based metadata browser to enable users of the Enterprise GIS to see what data is stored in the system by users from other departments. Viewing the metadata will enable you to determine if a data set meets your particular needs, and if so, you can then contact the data owner to request read privileges be granted to your ArcSDE account. Note that you'll need an ArcSDE account first (see the Support section for instructions on creating an account.
Check back soon for our metadata browser!