Whenever you visit a webpage on your iPhone or other iOS device using Safari, check the url or address bar for the "Reader View Available" message that will show briefly. You can then tap the icon in the upper left corner to enable Reader Mode. This will strip the site down to just text and images and remove most ads and other details of a website that distract from reading the text of the article. Once you're using Reader Mode, tap the "aA" icon in the upper right. New in iOS 9, you can now change the text size, typeface, and background. Pretty nifty!
Here's a GIF showing the steps.