Is the to be consumed webservice REST or SOAP based? There already is a lot of information for this available on both the Mendix site and this forum.
For SOAP, check out: https://world.mendix.com/display/howto40/Consume+a+web+service
For REST webservices you will need the RESTServices module from the AppStore. This comes with documentation of how to get your first GET JSON based webservice working.
You can use Java (see here for more information) to extend a Mendix application's functionality beyond the basics offered in the Mendix Business Modeler itself. Connecting with external API's is one such example of where Java extensions usually come into play.