try using a css reset like the eric meyer reset or the YUI reset. will help but no easy or perfect way to make things look identical in every browser
It is time consuming at first, especially if you are stilling learning the ropes of DIV+CSS. However after you've done enough practice and met enough of problems and got them all solved, you will have the knowledge of what WORKS and what DOESN'T WORK.
It is then you know how to write the most compatible style possible in the first place, thus saving all the time in degugging and rarely have any problems with any of the major modern browsers: IE6, IE7, FF2, FF3, Opera 9, Safari 3 Win / Mac.
Yes, it is possible and as easy as it can get. Practice and conquer them one by one, then you know how to do things right in the first attempt.
Well the only baffling monster should be IE6 I guess. It's inbrowser. Other than that, ff2, ff3, opera 9, safari win / mac, ie7, ie8 are relatively similar in the rendering engine, at least with much less bugs than it has with IE6.
I have a few best practices for you (one who has just begun their trip in CSS) in coding to get the max CSS compatibility:
If it needs to be pixel-perfect, then you'll need to use px in your stylesheets. Use a css reset stylesheet, then size everything based on pixels.
To ensure that your css is rendering correctly in different browsers, you might find a service like BrowserShots useful, however, I think you'll find it very difficult to get absolute consistency across all browsers.
My personal preference is to use correct markup and css, leave out any browserhacks, and design layouts to degrade gracefully.