There is a tutorial that shows you how to use maven to start an embedded instance of tomcat and run tests against your service using RestAssured:
http://www.hascode.com/2011/09/rest-assured-vs-jersey-test-framework-testing-your-restful-web-services/
You start tomcat in one shell and run your tests in another.
However, I strongly recommend using the jersey test framework which transparently spins up an embedded container. In this case you wouldn't use RestAssured at all, but the jersey test client. Your tests will run more quickly and with less fuss. It's well documented here: https://jersey.github.io/documentation/latest/test-framework.html. The tutorial also demonstrates this approach, though it doesn't seem to me that the client is correctly constructed.
In the past I've also tested REST resources by calling the implementing class methods directly. Though this doesn't test the correct mapping of the http query parameters/body to java method parameters, it was often sufficient (especially when I'm also coding the client side code).
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