Getting on a ballot requires petitioning, or collecting signatures from neighbors. Every County Committee seat is up for election in every even-numbered year, and the petitioning window is usually February through March. The minimum requirement is to collect signatures from 5% of the registered Democrats in your Election District. As the number of voters in each Election District varies, the number of signatures required varies, but it's usually somewhere between 30 and 60 signatures.
Then you need to file the signatures with the Board of Elections. If there are more candidates than there are available seats in your election districts, the candidates will appear on the primary ballot for the voters to choose, but most county committee members run unopposed and don't appear on the ballot.
Rep Your Block was created to help Brooklynites run for County Committee, and they do an excellent job guiding candidates through every step of the process. Sign up at RepYourBlock.com and they'll reach out to you with more information.