Libraries are usually very cooperative in sharing their policies and procedures so it might be best to check with a local library that already has a Library Telescope Program so your library is in sync with local practice. You can find libraries that have Library Telescope Programs at Locations Here are several examples that are available on library websites. Gunnison County Libraries, Gunnison CO: Lincoln Public Library, MA: Freedom Public Library, Freedom NH: Microsoft Word - Telescope Lending Policy 2-16-17.doc ( Scotch Plains Public Library, Scotch Plains NJ: Massapequa Public Library, Massapequa NY:
Generally, the following should be checked at check-out and check-in: Ensure that the contents of the belt pack are present: the instructions, the constellation guide, and the red light. Check the viewfinder and make sure the battery is still working. Be sure to turn it off. This is the biggest problem with the Library Telescope that patrons forget to turn off the viewfinder draining the battery. The library should have extra viewfinder batteries on hand to replace as needed. They are not very expensive. (Most, but not all, LTP scopes use a battery pack of AA batteries. These are more forgiving than the button batteries.) Check that the viewfinder is correctly aligned with the telescope. Often patrons will turn the alignment screws on the viewfinder causing it to be misaligned. (The instruction manual explains how the user can adjust the red dot finder if needed.) Visually inspect the telescope for possible damage: cracked laminate, dents in tube, loose parts, etc. 
Most libraries lend the Library Telescope for 1 week although some use 2 or even 3 weeks.
We want kids to use the telescope, but we want adults to take responsibility for borrowing and use. Libraries generally only allow adult patrons to borrow the Library Telescope. Libraries vary on use of age 18 or 21.
It is not generally required but it would be best if patrons borrowing the Library Telescope have attended patron training or viewed a video on use of the Library Telescope. As stated above, the skills needed to “run” a LTP are well within the grasp of most non-astronomers. The telescope and instructions are designed to allow a novice to be successful in a short amount of time. Plus, there are many resources on the web for learning how to use the telescope and find fascinating things to view.