I would like to know what all skills are required to design different types of websites.
It depends on what you mean by "design."
Since you posted in this forum, I'm assuming you mean graphic design- page layout, graphics, etc. If so, the designer would need to have artistic skills and the ability to use whatever graphics program you use in-house (most like Photoshop?). He/she should also be able to design for functionality, not just show. If he/she will also be building web pages, then HTML and CSS are also definite requirements. Being able to work with different types of people (clients, upper management, sales people, programmers, etc.) and convert their needs/wants into a finished product is also critical.