Chatwoot's API lives at https://app.chatwoot.com/api/v1 for Chatwoot Cloud, or on your own server if you self-host. Most paths include your account id.
Copy your access token from Profile Settings in Chatwoot and send it as the api_access_token header. In the examples it's written {{CHATWOOT_TOKEN}}.
Full reference: https://developers.chatwoot.com/api-reference/introduction
Includes your accounts and their ids.
curl https://app.chatwoot.com/api/v1/profile \
-H "api_access_token: {{CHATWOOT_TOKEN}}"
curl "https://app.chatwoot.com/api/v1/accounts/{{ACCOUNT_ID}}/conversations?status=open" \
-H "api_access_token: {{CHATWOOT_TOKEN}}"
curl -X POST https://app.chatwoot.com/api/v1/accounts/{{ACCOUNT_ID}}/conversations/{{CONVERSATION_ID}}/messages \
-H "api_access_token: {{CHATWOOT_TOKEN}}" \
-H "Content-Type: application/json" \
-d '{"content": "Thanks — looking into it now.", "message_type": "outgoing"}'