First create an artificial "extreme" example with an identical passage of text.
Lay the first out to be as unreadable as you can... pick a fancy display font set to a small size, make line space very wide, reduce line spacing and decrease contrast of text vs background (e.g. light gray font on white bg).
Lay the second at the same font size with a web optimized san serif font using techniques to enhance readability.
Then show an "in situ" example.
Take something from your project that you feel requires work. Clean it up. Then do a before and after comparison. Show them those and point out what you did and how did helped readability.
Wrap up with the benefits and costs
Then you close up with how you feel improving readability will help users with their workflow etc. Might want to point out how much time it took you to fix up the "in situ" example. How does it translate to effort if the team does it everywhere.
Then you can field additional questions if they have any.
Good luck with it. Typography is an important part of design. :)