Is there any genuine method following which I can use css positioning without giving any consideration to browsers?
Nowadays, most of your considerations is about how to follow the standards, and not how browsers interpret them. Some browsers have somewhat weird implementations of standards, such as MSIE. But they are getting better :) (almost good now with IE7 and 8!)
So to answer your question: Consider not foremost browser issues, but the web standard compliance of your code. But, to some extend also the somewhat quirky implementations of standards a few browsers might have.
Max the design for the majority, but don't forget the minority. Knowledge and tricks are good to a certain point, beyond that, to make really stunning design across plattforms, you need understanding of how the rendering engines of different browsers think and work.
user-centric, future-proof designs start with standards.
then you extend for your exceptions (IE 6 and other rarities)
But my visitors won't appreciate it if my website follows the coding standards but everything is overlapped. And it is the visitor I am targeting mate, not the programmers and web developers.
I have found invented one method though, if you follow the following website: www.victorypayday.com
You would see I have created the entire website with division positioning and never in the code is any caring for any browser.
But again, that method requires one to use table in the lowest bit otherwise website loses flexibility of size.
I like (and found very informative) the Yahoo grading system for browsers. It really put in order something that is just bloody obvious:
So you do what you can to make it passable in the Grade-A browsers, and worry not-so-much about the rest :)
Hey and I (still) strongly suggest reading the Zeldman book, it's so informative about this stuff.
You might experiment with flexible dimensions (ems) in a mainly text-based layout, but once you have images that also becomes fragile since images are dimensioned in pixels and do not scale with font size. Even then, the width of a box and which font from the stack is used might make a difference of 2 or three lines in a paragraph as text is flowed.
Although floats have less ability to be positioned, they have the powerful capability of containment, and the innate ability to keep out of each other's way (most of the time).