Generate a Marketing API key from Account & billing > Extras > API keys. The key's suffix tells you which data center your account lives on, which matters because every API call has to hit that specific data center's URL, a common first mistake when wiring up an integration by hand.
The API itself is well documented and covers list and audience management, campaign creation and sending, automation enrollment, and reporting data pulled back out. It's the foundation almost all custom Mailchimp integration work builds on, including the CRM and e-commerce syncs described on our Mailchimp integrations page →.
Webhooks run the other direction: Mailchimp calls a URL you provide when something happens (a subscribe, an unsubscribe, a campaign send), which is how you get real-time Mailchimp events into another system without polling the API on a schedule.