How to support the arts is a question that has two answers, depending how you answer this question: are you rich?
If you are wealthy enough to do so, the best way to support the arts is to give generously to their cause. Whether it is making contributions to overarching organizations that provide grants for the local artists or directly to the individual groups is up to you. You might choose to sponsor scholarships at art schools, for example.
If you are not rich, then you have a few different options. Of course, actually attending the events is important: go to art openings and gallery shows to show your support and interest, or buy tickets and attend the performing arts events that are to your tastes. By buying tickets you not only fill up a seat and let people know they have an audience, but you fund them the money they need to make it happen. Give small donations when and if you can.
Another way to help the arts is to volunteer your time. Whether you are an usher at a show, or in the production group, it helps people to lower the overhead costs. You can also do some free advertising, or help out by offering any skills or services you are able to provide. For example, if you're great with graphic design, why not offer to design posters and fliers? Help dancers sew costumes or offer to work the box office at an upcoming event.
You might also be able to help them by finding corporate sponsorship. If you don't have the money to give them, perhaps the company you work for does. There are so many ways that you can help support your local arts community. Look into the local groups who are already doing so, and see if they have a place where you could step in and help out.