So, what is the problem? You already know what you need to do.
1. Place two textboxes with calendar extender and a button as you said.
2. Write logic to filter rows from database in the Button click event. Query like
SELECT [column1],[column2],[column3],[...]
FROM YourTableName
WHERE [Date]>=@FromDate AND [Date]<=@ToDate
Here @FromDate and @ToDate are the values from the textboxes for date filter.
3. Now bind the GridView with the query result
That's all !