Fonts are installed on each machine used to view a website. The font or font family you want to display to your site visitors is stated in your site’s CSS. The reason for a font family or calling for several font styles is in case the machine viewing the site does not have the font called for in the CSS, installed in the viewing machine.
So, if you want to show an exact type font to your visitors and it is not commonly installed, they will not see it. Your Didot font is not a regularly installed fort. If you only need the type style in a small part of the site, you might consider using an image built with photoshop containing the font.
However, if you want large and especially dynamic areas of your site in your special font, you might try Google Fonts. It’s unlikely that you will find your exact font there BUT you may find something close enough to meet your needs.
If you find a font close enough to what you want, follow the directions you find on the Google font site about how to add the font to your website.