When I design websites, I typically try to design them in a way that will allow the site to be viewed well on any platform. However in some cases, usually due to server side programming or visual layout of the site, this is not possible. When those situations arise, I design a separate mobile version of the site using standardized mobile technologies like XHTML and JQuery mobile.
Content also needs to be considered when designing for mobile, as many people are using slower connections on plans that charge them for all of the data they download. Because of these factors, images must be smaller (in file size) and content must be organized in such a fashion that the user will only have to download what they are looking for.
I have also had experience in doing mobile versions for preexisting websites, that were not designed by me. If you already have a website and need it mobilized, I am quite proficient at re-envisioning websites for the mobile web.