A library is a separate piece of hardware that houses one or more tape drives and also has a magazine of some type, so that you do not need to manually mount tapes.
if you have stand-alone drives (which it sounds like you do) all you need to do is insert the cleaning tape, wait for the cycle to complete, then remove the tape
How long the cycle lasts depends on your hardware.
A couple of more points -
When you got it, each piece of cleaning media should have come with a label with a series of check boxes (usually 20 of them) Each time you use a cleaning tape, tick one box. When they are all ticked, toss the cleaning tape and start a new one.
If you have never cleaned your drive before, and are getting errors, run the cleaning tape through two or three times to start with.
Check your drive documentation for recommended cleaning intervals.