Cleaning of disks is something that many simply don't care too much about, as in most cases the disk is on hire from the local video shop or borrowed.
If however you own the disk that might well be the only mint condition master of an expensive imported movie it pays to clean the disks properly.
It should go without saying that ANY disk should go directly from it's container to the player and likewise from the player / PC back into it's container via a few fingers on the outside of the disk, it ain't hard, never putting a disk on the table, carpet, shirt, couch or whatever is handy, to start bypassing the container is a recipe for a scratched or ruined CD.
The good housekeeping basics aside, the only thing that should ever get on a CD is dust, apart from just blowing it off, the best and only good way to clean them is with a single / dual wheel rotary cleaner with a "very light" spray of isopropyl alcohol, these rotary cleaners are not expensive and pay for themself many thousands of times over, I have worn out 2.
To use your shirt is pure lazyness and should be avoided, plastic buttons will scratch a disk real quick, I have master disks here that are many years old and have been played 100 times and they are still as purchased, brand new, they always live in their case when not in a player, rest assured that if put on the coffee table they will eventually be dropped and just like buttered bread they always land data side down.
As for claening either the pickup head or disk, the proper cleaning disk or rotary cleaning unit is the only way, sure there are other incorrect ways but to do otherwise will scratch/mark the disk or damage the pickup head, it is only a simple habit to do the right thing, it is not hard.
Then again I do NOT EVER loan CD's, not even to my best friend, unless I am physically there, and even then the basics apply in advance, scratch or mark it in any way and you buy it, that may seem a tad rough but then again all my DVD's are still like brand new.