Woodpecker authenticates against your existing version control system (Github/Gitea/Gogs/GitLab etc). See the upstream docs for the supported providers.

For example, to use Gitea for authentication, create an OAuth2 application inside Gitea and edit /app/data/env.sh like so:
export WOODPECKER_GITEA=true
export WOODPECKER_GITEA_URL=https://gitea.domain.com
export WOODPECKER_GITEA_CLIENT=1950a7f0-74e1-4003-8d51-6253eb673940
export WOODPECKER_GITEA_SECRET=gto_kgoizrbde5qv242q2waw7hocb5sa5snafqhwoeownflb4lml7dsa

Be sure to restart the app after making any changes.

Info:
Only one auth provider can be active at a time. For example, if you enabled Gitea, make sure all other values like WOODPECKER_GITLAB are removed or set to false.