A REST Web Service uses http verbs (GET, POST, PUT, PATCH, DELETE) to do various actions. So to test a web-service you need to write tests that send these requests with the appropriate data for your web-service and then examine the results. There are various test frameworks that make your life simpler.
Take a look at some simple tests I wrote for a sample REST Web-Service here.
The tests I wrote were for the purpose of running in Mocha but Jasmine should not be too different. Here is a great article on Jasmine and Mocha and the differences and similarities between them.