What are the necessary steps to begin developing in the Spring Framework?
1) Learn Spring
Ok. This is a tongue in cheek reply. Seriously though. You should start with an intro level Spring book. "Spring in Action" is easier to bite off than the official manual. As you read, try the examples. You want to get really comfortable with autowiring before going on to anything more complex.
Should a developer have a solid foundation in Core Java and if so, how proficient should said developer be in Core?
Yes. If you can't write simple Java and understand concepts like inheritance/interfaces/exceptions/etc, you'll struggle. I think you are past that already though.
On a side note, when is a developer ready to begin working in Java EE in general?
When you feel comfortable with basic Java. Note that JEE is a big topic. You are likely to be ready for servlets earlier than queues. There isn't really a right answer. If you are asking, you are probably ready. Try it. If something doesn't make sense, you'll know what you need to bone up on first.