Take a piece of cloth and blindfold yourself.

Now try to use your own website with a text-to-speech (TTS) engine and your keyboard.

No joke, recreating the users situations is often a cheap and easy way to find problems.

For example I like to check a design by setting the network speed limit with the browsers dev tool to 32kbps, to see how long it would take to load on a bad connection.

Curiously enough even using a command line Browser like lynx can be enlightening. You start to see all the crap.

I'd urge everybody to take a simple unstyled HTML page as a markup. If your page looks bad without styles, you are doing something wrong. If the navigation is cluttered and convoluted in unstyled mode you are doing something wrong.

If your page is less usable than a basic well structured HTML page, go back and make it a basic well structured HTML page and add styles from there.

Webaim has lots of good base level info: https://webaim.org/intro/

In the article most of the annoyances boil down to crappy html markup and unclear navigation. These are things that are easy to fix without any special accessibility knowledge and go a long way in improving usability for everyone.

As a rule of thumb, make sure the site works with Lynx. If it does, then you probably won't need anything but minor adjustments.

Or browse the site with CSS styling turned off. Firefox also has an accessibility developer mode (Shift-F12) but it mostly focuses on technical issues.