Dear Rose --
What you can do is to refer to the school's HR department for a set guideline and rules on supervision. Do they have a supervisory program for all faculty and staff that managers of each department can follow? What expectations do they have of librarians? Are there indicators for assessment and evaluation of performance? Most schools have. Use this as your guide. If you are supervising your librarians, refer to their job description next.
Create a list of focus areas that merges the school's standards on performance and the librarian's or staff's expected job description. This is for your perusal. This comes in handy during supervision and monitoring where notes can be written or documented. In time, this could be used as your reference when finalizing a report or document during staff evaluation and rating purposes.
There are performance instruments as well. These are made by the HR department. It has, basically, three components -- Professional Competence; Work Ethics; Personal and Community Relationship.
Remember that supervision is two-way. It can be directed by you, as supervisor, or by them as independent workers. It would depend on the librarian's or library staff's level of experience, competence and yes, EQ. For senior staff, they can be self-directed, meaning, they can set their own goals and objectives at work. They can also be depended upon to manage their time better. Therefore, monitoring and supervision of their work can be done periodically, say once a quarter or semestral. Or, their report on the work they do is enough for you to know that they deliver. If not, then change strategy. There are cases when supervising a senior staff is like mentoring a newbie or worse.
For newbies and junior staff, more frequent monitoring and supervision should be done until such time when they manifest self-directed work skills and ethics.
What will you supervise and how? Begin with assessment of their skills. We're talking of library skills here inclusive of basic communication skills. You may also refer to past performance records of the staff. That's a starting point to assessment. Focus on areas that need improvement in a given time - six months, one year, etc. What measurements will you employ to see improvements or otherwise. Rating scale? Narrative reports? This must be clear.
When these are identified - areas of focus, indicators and measurement, speak with the staff and work together. Staff should also be aware of his or her weakness and strength. The result of your dialogue becomes the supervisory plan for that staff. The accumulated supervisory plan for each staff becomes the supervisory program.
The trick here is that, you, as library manager, must be able to set individual objectives leading to the attainment of library goals. You act as conductor giving direction and achieving harmony. It's not so much as who is doing the job or not, but seeing to it that library goals and objectives are achieved by the people you've entrusted to do the work. Praise when necessary. Manage behavior as needed. Managing and mentoring people can be tough, but keep trying. I wish you all the best!