Testing existing application with chrome, safari, mozilla firefox

There is an asp.net application which was compatible with IE only and now has been converted to work with Chrome and other browsers. So for the testing point of view, what type of testing and strategies should required to test the whole application and also we are going to use selenium. I want answer in brief like how do I start, what would be the challenges may come and how do I proceed? I am like in the beginning of the testing phase.