If you are a Coveo Cloud customer, the REST API can be accessed through the Coveo Cloud Platform. More information is available in the Search API section, including the URLs to use and how to authenticate.
If you are using an on-premises Coveo index, you will need to deploy the REST Search API locally. There are many ways to do so, depending on your specific use case. Refer to the On-Premises section for installation and usage instructions.
The REST Search API supports many means of authenticating clients. Those means differ depending on the kind of deployment, so refer to the section about your particular situation for details on how to implement authentication.
The REST Search API implements a Query Pipeline that can be used to extend how queries are performed (see Managing the Query Pipeline).