Monetizing APIs can be efficiently achieved using platforms like Moesif, which simplifies the process of charging based on unique user access. By integrating APIs with Moesif, businesses can quickly establish a monetization model, such as a $7 per month fee for each user, with Stripe as the billing provider. Moesif enables the creation of plans and pricing structures, allowing businesses to track and report API usage accurately. The process involves setting up a billing meter to monitor unique users, with usage data seamlessly reported to Stripe for billing purposes. This integration facilitates a streamlined approach to API monetization, making it accessible and efficient for companies looking to accelerate their API revenue streams.