There are two items here - negative test cases and reading the log of these errors.
The first item (Negative Test Cases) is not specific to WinRunner as it is a testing method which is able to be applied manually or in any other tool. The designing of this test will depend on the application requirements. We can't tell you how to enter this information without knowing the application.
As for the script being able to read and log the errors, well this is something directly we can't answer without knowing much more than the general statement:
<ul type="square">[*]How does you application handle errors? It is a popup, a marking to a log file, or a shutting down?[*]Can you read this information in the instance of a positive test?[*]How does performing a negative test differ from performing a positive test other than the intent of the results of the test?[*]etc[/list]
This thought process isn't tied to the tool you are using, it is a concept used even in Manual testing. Have you designed these tests in your Manual Testing career prior to this automation effort? What steps would you need to take to verify the tests?
Answer that and then you can move to programming the tool to perform the tasks in an automated fashion. Without being able to impart the steps of what you are trying to do no one will be able to truly help you in your situation. It is like answering "how long is a piece of string?"
Take a step back and if you have more specific questions on the steps to code I am sure I or someone else will be able to help somewhat as most of us no longer use WinRunner and are relying on past memories since the tool is no longer supported from HP and is superseded with QuickTest Pro.
Insanity: doing the same thing over and over again and expecting different results