Address autocomplete happens when a visitor on your website starts typing their street number and a few characters of their street name, and is then shown a list of suggested addresses. They then select their address from the list, resulting in a much faster and more accurate process than them entering their street number, street name, suburb, city, state and post code manually.
Two of the main global services are Google Places and Mapbox Geocoding.
Pricing for Google Places and Mapbox Geocoding are on a per request basis.
https://cloud.google.com/maps-platform/pricing/sheet/
https://www.mapbox.com/pricing/#search
If you are comfortable working with API services, then it's a relatively simple process of signing up and following the documentation.
Google Places - sign up and documentation
Create an account - https://console.cloud.google.com
Documentation - https://developers.google.com/maps/documentation/places/web-service/autocomplete
Mapbox Geocoding - sign up and documentation
Create an account - https://account.mapbox.com/auth/signup/
Documentation - https://docs.mapbox.com/api/search/geocoding/