Surprisingly, screen-readers don't require much attention, so just mark up text using the proper HTML tags, label your images, avoid moving focus, and avoid dynamic changes to the pages. Some websites include a link that is only accessible by screen readers to jump to the page's content area, but this isn't strictly necessary if you use landmarks and, most importantly, mark headings as such, because the first thing I do when I browse a news website for the first time is to try to jump directly to the highest order heading I can find.

Use semantic HTML from the get go. From there try and use progressive enhancement.

I'm not visually impaired but my grandad is and uses a screen reader - but the screen reader reads every bit of code in the web page. It drives him crazy! He's never seen a web page as he lost his sight almost completely about 20/30 years ago, so it's really difficult for him to navigate a page. This could be useless input but i only subscribe to this sub to watch out for stuff that might be of use to him so thought I'd chip in.