On my CV I have added png icons and resized them
When export as pdf these icons lose resolution/quality
How do I fix this?
Since this is a CV, I suspect you're doing it in Word, which doesn't handle resizing of pngs very well. (I'm being overly benign saying it that way. Word's sadistic treatment of innocent raster images is worthy of a trial at The Hague.) The open source clones aren't better.
Follow DA01's advice and skip the icons, or find some EPS versions (or, better yet, use an actual font like webdings).
You don't mention the software being used.
When you are working in Photoshop, you are working with pixels only (aka dots). When you export to PDF, you are creating a document which is going to be printed with a presumed fixed real-world dimension (such as 8.5 x 11 inches). This is where the number of available dots comes into play, because the quality is entirely a measue of how many pixels you provide.
The PNG image in both the display case and the printed case can be thought of as being a grid, but the grid on paper has far smaller measurable dimensions for the same number of squares in the grid, so to maintain the proper scale, the grid must be stretched larger. This means that the export to PDF is a second resize. The type does not tend to suffere from this problem becasue it is not stored as a grid (typically), but rather as "math" which only gets set to a grid at the moment of printing, so the resolution is always the best possible for the output.
For technical reasons which have more to do with commercial printing, the typical number quoted for images to be printed is 300 dpi for color and 600 dpi for greyscale (B&W).
This means that if you want an icon to be .25 inches square on paper/PDF, the image must be 75 pixels wide and 75 pixels high (150px square for 600dpi) minimum.
If you are working totally in Photoshop or other raster image editing software, you need to have (8.5in * 300px) x (11in * 300px) pixels in your document. Otherwise, just tailor the individual placed images this way.
Note: for raster images the dpi is just a tag for software as long as the pixels are there the "DPI setting" is not important
Use an icon font. I can't recommend one in particular, but this might help: http://fontello.com/