The Learning Center lists their guidelines:
"To apply for the HubPages Apprenticeship Program, you must have a HubPages account and at least one published Hub. You must also have an approved Google AdSense account and be enrolled in the HubPages Earnings Program."
"we will be looking for a consistent stream of newly-published Hubs and/or an already existing blog, website, or collection of published online work. We will be reviewing this work for proper grammar and punctuation, as strong writing skills are essential for success, and the Apprenticeship Program does not cover basic writing skills."
"Finally, we are looking for applicants who are motivated to improve their online writing skills and build their online brand, and are also willing to learn and provide support and feedback to fellow Apprentices... we only want to accept applicants who are willing to invest a significant amount of time and focus."
I have read elsewhere that while you are waiting to be accepted into the program, you should write at least 5 hubs a month to show that you are capable of the type of volume the program requires. All of your hubs (or other online writing) must show that you are capable of writing quality content.
In addition, if I were choosing, I would choose people who show themselves as good members of the community. I would think that if someone regularly talked down all of HubPages programs, or attacked other Hubbers, they would not be invited, since part of the program involves group feedback. This last paragraph is just my opinion - I don't know if that is actually the case.