For a standalone drive, you do indeed just insert a cleaning tape, let it run, then remove.
Most Cleaning Tapes are good for 20 passes, and come with a label that has 20 check boxes on it. Check one box after each run, and toss when you check the 20th
If you have been overusing one old cleaning tape, get a new one and try several consecutive passes (checking a box for each pass) and see what happens
(Most drive manufactuters recommend that you not run cleaning job until the "Clean" light on the drive comes on, since the tapes are mildly abrasive, and over-cleaning can shorten the life of the Read/Write heads)