How does a candidate who is NOT a democrat or republician get their name on a ballot for a general election?

Each state has its own rules for Independent or third party candidates. Usually the deadlines are the same for these and for the two big parties, but many of these deadlines to file or to become eligible to file as in the case of third parties are not well known by the general public.

The best way to get an answer you can actually use is to call the Secretary of State's office in your state capital and ask what the rules are.

Many states have levels of government that are non-partisan where party affiliation is not required, or even noted, in elections.