First test your site in Firefox, if it looks OK validate it to get rid of any errors you may have missed using http://validator.w3.org/
Then test in Safari, Chrome, IE8, 7 and 6, you can always use an IE specific style sheet to deal with any IE quirks that may arise and below IE8 you will probably have a few.
It doesn’t really matter which order you do it in, but do validate your site before troubleshooting and test both cross browser and cross platform as they do not always perform the same way.
The major difference between two versions of the same browser is their support for newer portions of the HTML language, A new browser is generally better at displaying Web pages than an old one.
However, Internet users tend to upgrade their browser based on the addition of new features, like email integration and instant messaging, If a user doesn’t care about these features, they’re happy to keep surfing the Web with their old browser,The term cross-browser is often confused with multi-browser. Multi-browser means something works with several web browsers. Cross-browser means something works with all versions of all browsers to have existed since the web began,you can use this html code for a cross-browser <div id="sample" style="position: absolute; top: 100px; left: 100px;">some text</div>.
First, understand that it’s hard to build a Web page that displays perfectly on every version of every browser running on every computer. And doing so may require you to leave out features that you really, really want to have on your Web page. Building a Web page that’s compatible with Version 1.0 of every browser would mean building a bland page filled with plain text.