If my customer does not know how to write the UAT test cases I would do the following
1. Suggest a template for UAT test plan that is minimalistic in nature. It would address some setup and environment issues suggested use cases and include test cases.
2. If I have the time I would discuss with the customer about the features they think are most important. I would further clarify if they have any use cases or stories about the features that can help me identify the test cases. I can use this discussion to identify test cases I might already have created during the internal testing process or would have to write new ones.
3. The minimum I can do is to select a bunch of my test cases club a few related ones into more high-level test cases and give them to the user. This is if I do nto have the time (or for that matter the inclination) to discuss with them what I described in step 2.
In practice it may be more important to drive the UAT and to get the customers to actually spend the time on UAT rather than defining the tests. Customer susually have some idea of what they want. If they do not God save you and your customer!