There are two ways to change the law: by legislative action and/or judicial action. In other words, one can get laws passed, and/or can push a case to a judgment in court.
It is amazingly easy to get a lawmaker interested in proposing a new law. It only takes several letters from about three constituents to start the fire. From there, however, you need to help the lawmaker to get the votes needed to pass the bill. To learn how to get a law passed from the grassroots to the finish line, it is suggested that you read Isaac, Katherine, CIVICS FOR DEMOCRACY (Essential Books, 1992, ISBN 0-936758-32-5).
A court case is important to the litigants themselves (i.e., to the plaintiff(s) and defendant(s)) but usually of little or no impact to other people. The reason has to do with the nature of judicial remedies: they have little value to people other than the litigants unless a case goes on appeal and the higher court publishes its decision. Even if a case is won in court, it normally would have little or no impact unless it were appealed to a higher court and the decision were published.