Following tips will help you to make a cross-browser compatible website as all leading browsers such as Internet Explorer, Firefox, Google Chrome, Opera etc are starting to base their markup formatting on W3C standards:
1. Firstly, HTML 4.01 is outdated and the current standard is XHTML 1.0. There are not a lot of differences between the two but what ever differences there are are very important. Please refer to the W3C XHTML standard.
2. W3C also provides a markup validation service which you should use to validate your markup on a regular basis. Chances are that you will face a lot of errors and problems the first time you validate your page but you will learn a lot.
3. It is also a good idea to browse through the W3C CSS standard as that will help you maintain the consistency of the appearance of your page and controls across all browsers.
4. Try to control all your positioning and styling through your CSS and use tables as less as possible.
Hope the above points help you to make better cross-browser compatible websites in the future.