The best verb here is "apply" She applied sun tan lotion on her shoulders. You can also use "put" in a less formal context. She put sun tan lotion on her shoulders. "Smear" is used when you put an oily or greasy substance on a surface like jam on bread etc. "Spread" can also be used this way.

There are many ways to describe how an activity is done. I feel there is a best way to say something- and it is the way that describes the action. She smeared it = She did it without much care She spread it = she applied it evenly and has not yet rubbed it in She applied it = vague - non-descriptive. Was it sprayed on? Was it rubbed on? This is fine when you do not want that action to be imagined to thoroughly because you are focussing on some other issue. She rubbed it in = She may have taken her time and made it go away. She sprayed it on = She has a mister she poured it on = she uses a lot She squeezed it on = she did not rub it in yet So, the point here is that a word is not best unless it is describing what you want at the level you want it described.

It's better to say: She rubbed sun tan lotion onto her shoulders.