All you have to do is change the domain part of any API requests your application makes from "apis.berkeley.edu" to "gateway.api.berkeley.edu" For example, the request "GET https://apis.berkeley.edu/sis/v2/students/61889?id-type=campus-uid" should be changed to "GET https://gateway.api.berkeley.edu/sis/v2/students/61889?id-type=campus-uid". If you've set the host domain as a constant in your application code, this should be a snap!
Be sure to make this change in your pre-production test environment first and run tests that cover all of your use cases. The new gateway does have additional layers of security, including a web application firewall, so some edge cases won't work like they did on the deprecated gateway. For example, it rejects API calls that don't include the standard "Accept" and "User-Agent" header parameters (see the FAQ on requests that worked before but get error responses on new gateway for more details).
Also, since the new gateway is cloud-based, if your application is hosted in RFC1918 address space (e.g 10.0.0.0/8) you'll need to use a proxy or NAT service (see the Known Issue on RFC1918 networks for details.)
If you're having any difficulty using the new gateway, please let us know by emailing eis-support@berkeley.edu or slacking us at #api-transition-help Include what network/IP address your application is using, the app_id used, and the timeframe in which you made the troublesome requests, along with the nature of the errors you're seeing.