While politicians and Court watchers are sharing their opinions freely, you can read up on the process itself. A Congressional Research Service report called Supreme Court Appointment Process: Roles of the President, Judiciary Committee, and Senate (Feb. 19, 2010).
For a deeper dive into the subject, see also these additional CRS reports, available on HeinOnline [UW Restricted]:
- Supreme Court Appointment Process: Consideration by the Senate Judiciary Committee (Oct. 19, 2015).
- Supreme Court Appointment Process: President's Selection of a Nominee (Oct. 19, 2015).
- Supreme Court Appointment Process: Senate Debate and Confirmation Vote (Oct. 19, 2015).
The Federation of American Scientists' free website also provides copies of these and other CRS reports on nominations to the Supreme Court.
And for even more references to CRS reports, books, nomination hearings, and related information, see the Gallagher guide on Supreme Court Nominations: The Nomination & Confirmation Process.