It depends - what I'd do with test cases for a tester who wasn't familiar with a web application to be marketed to the general public is quite different from what I'd do with test cases for a tester who wasn't familiar with a business-to-business application that's never used by anyone except trained users. I would also write test cases differently for someone who is an experienced tester than I would for someone with little or no testing experience.
Other factors in how I write test cases in this situation would include how stable the application interface is - are menu structures, user permissions required and the like expected to change? - the kind of testing being performed - is this user acceptance testing, functional testing, integration testing, system testing, cross browser testing? - the scope of the testing - single feature, whole application, or something in between? - whether the tester needs to set up the application in test and generate test data or this is provided, and many other factors.
About the only constant I'd say is that there would be more information provided in the test cases - but exactly how much more detail I go into will depend on all the things I've listed above (as well as anything else that seems relevant).
For me it would make a big difference knowing how good the person is at following instructions and being perceptive. If I have worked with the audience before, I would write it at their level or way they understand. If it is for unknown people to run, I'd have to make it more simple and try it out on other testers before giving it to the real group that will be using it.