In addition to what was explained above.

["с" + instrumental] and [instrumental with no preposition] have completely different meanings. Some examples to illustrate the difference:

Он работает молотком. - He works with a hammer (by means of a hammer, using a hammer). Here "молоток" is a tool he uses to perform the action.
Он работает с улыбкой. - He works with a smile. "Улыбка" is not a tool, is it?

Он помог мне с улыбкой. - He helped me with a smile. (He was smiling while helping me).
Он помог мне улыбкой. - He helped me with his smile. (It is his smile which helped me. He smiled, and that helped me).

The instrumental can express a means of transportation as well:

Он путешествовал самолётом. - He travelled by plane. ("самолёт" is a tool he used for travelling).
Он путешествовал с самолётом. - He travelled with a plane. (Probably, he might have a small toy plane in his baggage).

The instrumental can express a role someone plays:

Я работаю инженером. - I work as an engineer (I am an engineer).
Я работаю с инженером. - I work with an engineer. (An engineer and I are doing some work together).

Он был архитектором. - He was an architect. (He played a role of an architect).
Он был с архитектором. - He was (together) with an architect (somewhere).