Art influences culture in many different ways. Here are some ways:
1. Art is often tied to cutting edge thought in society. Art is often cutting edge and eventually its comes down to the people. So, the link between high art and culture might not be immediate, but in time it comes.
2. Popular are is much more immediate. The most immediate medium is through movies. A blockbuster immediately influences people and trends. It also influences vocabulary, fashion and tastes. Also consider a hit TV show like friends. People wanted to be a part of NYC.
3. If we include music in the arts, we see that music can capture and share a generation. Think of rock in roll as a culture of rebellions, etc.
These points should get you started.
Art definitely influences our contemporary cullture because we are constantly exposed to versions of art expression in everything we see.
We are visual people in general, and we are affected by what we see.
What people do is often based on how we react to presentations before us. Our minds interpret and influence contemporary culture as we connect or disconnect from art.
It is the choices we make that are the greatest influence.
From another perspective, art is everything. There really is not anything that is not art.
The elements that make everything art, is that everything has a real presence and we are of course influenced by everything.
Art is not always beautiful, or limiting in its scope. Art is always influential because it is real and anything that is real effects our culture.