I use all three major browsers. Most of the visitors on my site are using firefox. So I first designed my site with firefox. After I have a functioning model, I then try to get it to work in Internet Explorer.
For my last javascript project
An online calculator - gridter.com: links, just the links
after I made a functioning model in firefox, it took me 2 weeks to get a similar working model in Internet Explorer. If you look at my webpage, you'll see that I couldn't find a way to get the same effect on both IE and Firefox, so I just had to make two different copies - one for Internet Explorer and one for Firefox (and most other browsers).
Overall, I've found that Opera is intermediate between firefox and Internet Explorer. If I can get something to work in both Internet Explorer, and Firefox, it should also work in Opera and just about every other browser out there!
You should first make sure everything works well for the browser used by most of your visitors, then, you should try to make things compatable with other browsers.