I want to design the architecture of .net web application.how to decide which pattern have to use as per scenario wise? Let say for banking or payroll system like application.
If you've not seen this already take a look at http://www.dofactory.com/Patterns/Patterns.aspx
Includes most common design patterns and also includes UML diagrams and real world examples.
I understand why you are looking for a 'design pattern' before starting out on a new project, but you would really need to focus in on particular aspects of the system before knowing what kind of design pattern to investigate, for example I recommend you investigate Model View Controller when talking about ASP.NET web applications, and looking into Inversion of Control to name but two.
One recommendation would be to make http://sharparchitecture.net/ your first port of call. Download and study this - don't just start using it blindly. It can be a great starting point for a new project and will introduce you to most of the patterns you will need to encounter.
DC