You will be utilizing Wrangler for local development to emulate the Cloudflare runtime. This is already wired up in your package.json as the dev script:
# start the remix dev server and wrangler
$ npm run devOpen up http://127.0.0.1:8788 and you should be ready to go!
Cloudflare Pages are currently only deployable through their Git provider integrations.
If you don't already have an account, then create a Cloudflare account here and after verifying your email address with Cloudflare, go to your dashboard and follow the Cloudflare Pages deployment guide.
Configure the "Build command" should be set to npm run build, and the "Build output directory" should be set to public.