Oracle monitoring db status
What is 'normal' will depend on your situation. An OLTP database and a warehouse will have very different usage profiles.

If you use a connection pool, then you probably don't expect to see a wide variation in the number of connections or sessions. Such a change would indicate a problem.

Generally you are best off looking for dramatic changes in your measures.

Grab SQL Developer 3 Early Adopter edition from the Oracle website. Check out some of the system reports, and look at the underlying SQLs.