In the US state of California, if someone feels an existing law gives excessive punishments or is unconstitutional, what can they do?
One approach is to sue the (state) government, to see if the state or US Supreme Courts agree. This is probably the most complicated way to get what you want, because it involves a lot of legal arguing, but you don't need a lot of people to agree with you, you just need the right people agreeing with you. Another approach is to change the relevant state statute (repeal, reword, add another); or, you could change the state's Constitution. Changes could either come via the legislature, or via the people. The role of the people, in the case of a legislative change, is to politically persuade the government to do what you want.
Via the initiative process you can eliminate the government-approval step by writing the desired change, then it gets voted on in an election if it qualifies (gets the necessary number of valid signatures: 8% of the last gubernatorial election). An example is Prop 1a (1966), which brought about a number of constitutional changes. There is in fact a distinction between an amendment and a revision, the latter being more extensive (Prop 1a was a large-scale revision). An example of a statutory change is this, Prop 12 (2018), which passed. Instead of collecting signatures, one can persuade a majority of the legislature, but this still requires voter approval.
The easiest path for changing the law is for the people to persuade the legislature, because the legislature has the power to change / add laws. Even then, some legislative acts have to also be submitted to popular vote for (dis)approval, either bond measures or amendments to previous voter initiatives.