There is no reliable, broadly applicable solution to this beyond testing, testing, testing. The issues are so complex that it's essentially impossible to build a tool that could do this for anything close to every possible difference between the browsers.
Incidentally; there is a tool called IETester that you can use to be able to run multiple, previous versions of IE.
EDIT: You (motto) and others have noted issues with IETester. While I have not experienced issues with it myself, that could very well be because I have simply not used it to help me with layouts that use things which happen to be buggy in IETester.
Comments below note that the Developer Toolbar in IE9 permits us to use the IE7/IE8 rendering engines. I would guess this to be a more reliable way to test layouts for those browsers, and I plan to begin using that instead, myself.
I will then likely keep using IETester just for assuring basic usability for IE6.