Vercel's REST API lives at https://api.vercel.com. Each endpoint has its own version number in the path. Add teamId= to act on a team rather than your personal account.
Get a token at vercel.com. Send it as Authorization: Bearer <token>. In the examples it's written {{VERCEL_TOKEN}}.
Full reference: https://vercel.com/docs/rest-api
curl https://api.vercel.com/v2/user \
-H "Authorization: Bearer {{VERCEL_TOKEN}}"
curl "https://api.vercel.com/v10/projects?limit=5" \
-H "Authorization: Bearer {{VERCEL_TOKEN}}"
curl "https://api.vercel.com/v6/deployments?limit=5" \
-H "Authorization: Bearer {{VERCEL_TOKEN}}"