I wouldn’t say that making it work in IE first and then check other sites is the right approach. Basically, after doing a number of sites, you kinda know what works and what doesn’t work in the various browsers. I actually work/test in Safari and Firefox, and most of the time my code works fine in IE — still, every now and then (when a big section is done) I check if it’s OK in IE as well, and then make changes if necessary.
I am one of those guys who doesn’t hate IE as much, because I’ve learned over the years what sort of things to avoid. Very basic example: if I have a design that contains rounded corners and I know beforehand that the site needs to be compatible with IE7, I sure as hell won’t use border-radius CSS code. Instead, I use images for that, and then when I check it in IE7, it looks fine. But still, I develop in Safari and Firefox.
It’s just a very basic example of how you should be clear to yourself what road to take, I guess.
And Dreamweaver…..? Um, no. ;)