If you use the product
Open API access in the product and request access: what it's for and the scopes it needs. Another person with approval rights approves it, and you reveal the token once.
If you don't use the product
Ask an admin of that product. They choose you from your organisation's People list (you need to be there, with your work email) under API access → Give an employee API access, pick the access you need and how long it lasts. You need no login and take no seat.
You then get an email with a one-time link, valid for 48 hours. It shows the token once; the token is never written in the email or shown to the admin. If the link says it has already been used and it wasn't you, tell the admin so they revoke it.
How to call the API: the developer documentation.