Wise's API runs on https://api.wise-sandbox.com for testing and https://api.wise.com for live. (The older transferwise.tech sandbox has been retired.) Most calls are scoped to a profile id.
Create an API token in your sandbox account's settings and send it as Authorization: Bearer <token>. In the examples it's written {{WISE_API_TOKEN}}.
Full reference: https://docs.wise.com/api-reference
Personal and business profiles, with their ids.
curl https://api.wise-sandbox.com/v2/profiles \
-H "Authorization: Bearer {{WISE_API_TOKEN}}"
curl "https://api.wise-sandbox.com/v4/profiles/{{PROFILE_ID}}/balances?types=STANDARD" \
-H "Authorization: Bearer {{WISE_API_TOKEN}}"
curl -X POST https://api.wise-sandbox.com/v3/profiles/{{PROFILE_ID}}/quotes \
-H "Authorization: Bearer {{WISE_API_TOKEN}}" \
-H "Content-Type: application/json" \
-d '{"sourceCurrency": "USD", "targetCurrency": "EUR", "sourceAmount": 100}'