Depends on what they are wearing and what kind of stethoscope I'm using. Mostly I find it's fine to auscultate though clothes although I admit this is not the best practice. However, it just normally isn't all that practical in some settings to have them remove their shirt and pants and undergarments if applicable to get a good listen to their chest, back, arm, belly, whatever. If I DON'T hear anything, of course I go ahead and slip my steth onto skin.
Here's the what I do, if I need to auscultate the lungs I typically go right on the skin, just slipping under there shirt. When i have to auscultate the heart i almost always go right on the skin because a lot the patients I see have a fairly thick fat pad over their left pec
If the patient is in a hospital gown, I auscultate lung sounds from the back first, directly on skin. If that's normal, I auscultate anteriorly through the gown. Any abnormals, I generally go to the skin to be certain I am hearing accurately.
Auscultating manual b/p's I always do on skin, after palpating first.
depends on the consciousness of the patient. If they are comatose or male Ill just go skin-to-skin, but if they are female and with it, or family is in the room, Ill just listen through the clothes. If I hear anything junky I assess further. Being in a hospital strips you of enough dignity/privacy as it is, so if I can still hear okay through clothes, I dont see the harm.
You should always auscultate on the skin as clothing can cause accoustic interference by friction with your stethoscope bell. Also so that you can inspect the patient visually and do your skin assessment!
However research has shown that applying greater downward pressure with the bell of your stethoscope can greatly reduce the amount of accoustic interference when auscultating, but ultimately I think it's better practice to auscultate on the skin.