<p>What is best way to allow user to pick date from a mobile device from usability prospective?</p>

Are you building WAP page in asp.net? You have a DatePicker control in the mobile toolset. On devices that supports it this will render as a regular date picker (as in regular asp.net) while on more limited devices it will render as a series of selectors where you first select the year, then the month and finally the date. Unless you have a good reason to do otherwise you should use this I think.