Great question! It ranges anywhere from 20 minutes to a full day.
It really comes down to a few things:
- The API you are working with. Some are simpler than others.
- Your developer's skill level.
- How you plan to use the service.
Check out this blog, API Integration: How Much Time to Set Aside, which goes into more detail.
You can also get a sense of what it takes to integrate from this video: