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I will recommend you to use a css framework. That will make your work very easy and cross browser compatibility is ensured by the framework itself. Just as an example bootstrap...
Minimize your work and have a life :)
First, webpage not nessecary to look the same in all browsers, specially when we are talking about old browsers (IE8 and below).
http://dowebsitesneedtolookexactlythesameineverybrowser.com/
For Modern browsers to easier to page look the same (Firefox, Chrome, Safari, etc..).
.box_with_rounder_corners { -moz-border-radius:6px; -webkit-border-radius:6px; border-radius:6px;}
Link below help you to generate the css3 code you need to support browsers:
For old IE browsers (IE8 and below):
a- using css3 workarounds (most probably the filter property), an examples below.
CSS3 Solutions for Internet Explorer
b- using a js plugin to support css3, like Modernizr, IE-CSS3, CSS3Pie, etc....