Developing Cross Browser support asp.net application

One way would be you write and test you application in different browsers that you want to support, there wont be to many(ofcourse there are some) differences in modern browser.
say you write a page on which you have javascript document.all, this wont work in many browser and therefore you should be using document.getElementById().
there is good enough material on internet you can use to find script and properties supported by all browsers.