For some reason I always forget how to do this, and most tutorials out there suggest wrapping your table in a container <div> tag but as long as you’re using <tbody> (and, ideally, not using <thead> or <tfoot>) then it’s easy with a small bit of CSS and no HTML changes at all.

The trick is to display your <table> as a block, and your <tbody> as a table!

Here’s the code. Fit it into whichever breakpoint makes sense for your site. Mine shown here is the standard phone width breakpoint for WordPress (782 pixels):

@media screen and (max-width: 782px) {

  table {
    display: block;
    overflow-x: auto;
    width: 100%;
  }

  table tbody {
    display: table;
    width: auto;
  }

}

Of course, right after I posted this I found that I had already written about it two years ago with a slightly different solution. Never hurts to have a slightly different perspective.