It does not change much in SAP. How you have been doing in other projects like .NET or other, you need to incorporate the same.
You need to send a POST or GET request to the intended service with the help of URL.
In order to get the URL, you need to seek help from the ABAP person who would be exposing the service to fetch the WSDL file for all the details about the service.
Once you have the WSDL, you can frame the request object with all required input parameters to make an AJAX call.