How to integrate a 300dpi design to a website

My designer gives me 300dpi design and when I try to get an image out of it, it is double or triple the dimensions of what it should be for the website

Also the font sizes are different, if I apply the font size of the design (psd) to my css, it does not match. The psd file font size is 13px while in css if I make it 48px, then it comes close to the design.

What should I do? how should I use the 300dpi design to integrate a normal website?