You can create a parameter in the filter section of the query that looks like this:
[Start Date] = ?current_date?
You can replace start date with whatever date field you want to use as the filter in the report: ?current_date? is a function in cognos that returns the current date and the question marks define that as a parameter. Then when you create the prompt page, reference this parameter in your date prompt and you will see the current date display as the default.
Hope this answers your question.
Dave Allen