This topic is way to broad for a Quick Questions & Answers forum. But I'll try to give you some basic idea, the way I see it.
This is usual stuff. The best you can do is to design the site which is not very sensitive to minor detail of rendering layouts in different layout engines.
To have and idea on those difference, you should experiment with different Web browser. To see what layout engines are available and what are the major differences, refer to these comparison articles:
So, the idea is not to achieve identical look — this is nearly impossible
and does not make a lot of sense. Your real goal in this respect should be to make your site looking good in all those engines, and, ideally, keep it recognizable, with its unique face.
How can you achieve that?
First, try provide high quality of design. This quality along is so rare, that it itself will give your site absolutely unique look. :-)
The most supportable rendering features are colors and fonts, but not layout, so base uniqueness of your site on the very thorough and clear color gamut and professional font decision (the less fonts, the better).
First and foremost, try to keep it simple. Remember that your main goal is interesting or useful content, good readability and transparent easy-to-understand navigation, and that all kind of decorations and effects only distract and irritate your users. Say "no" to complex layout. Keep the pages fluid. Don't allow yourself to add a single line, gradient, boundary between color tones or decorative element without some purpose which you can clearly formulate and which will be unambiguously recognizable. Please, no sounds, and, as a rule of thumb, no animated images moving without user's command, no pop-ups.