One tool I'd suggest looking into when getting started is Accessibility Insights for Web. A team at Microsoft developed a free, OSS browser extension for automatically detecting most common accessibility issues on your site: https://accessibilityinsights.io/docs/web/overview
Disclaimer: I do work at Microsoft, but my only affiliation with Accessibility Insights is as a happy customer :)
I immediately thought: how come none of the other browser vendors have something like this after all of this time?
Google develops Lighthouse, which, although an extension, I believe includes some a11y checks: https://developers.google.com/web/tools/lighthouse/
Similarly, Mozilla also promoted Webhint: https://webhint.io/ (which is cross-browser)
I'd also recommend Khan Academy's tota11y, which just works as a bookmarklet: https://khan.github.io/tota11y/