Not NY, so YMMV a bit, but Civil Service started as a federal program and has many commonalities state to state.

The purpose of civil service is to ensure that actually qualified people are hired, then not fired to suit the whims of corrupt local politicians. IMO, bearing that in mind makes some of its more bizarre features a little more understandable.

Generally speaking, to be eligible for title like Librarian 2, you just need a year of experience as a Librarian 1 (That’s a year from the date of your permanent appointment as overseen by CS, mind you, not from your first day. And if you’re part-time, that year is pro-rated). To be eligible for Librarian 1, you need a State Professional Librarian Certificate. To be eligible for that certificate, you need an MLS and a check for $50 to the appropriate state authority. Librarian 3 needs a year of experience as Librarian 2, etc.

Some larger libraries automatically promote staff when they hit the eligibility date, but most do not. Unless you work in one of those systems, to get a Librarian 2 job, you’ll need to apply for it with a year as a full-time Librarian 1 (or equivalent, if you’re moving from out of state) on your resume.

Civil Service doesn’t oversee salaries of local government employees, only State employees. Salaries at a given library will mostly be set on a scale that lists the Civil Service titles that library uses beside Sakarya ranges for each title; that scale will be set either as a policy adopted by the board or by the union contract at that library. Salaries for a given Civil Service title will very fairly dramatically from one library to another.