The best way to understand the requirements of Section 508 is to read through the text of it. Specifically 1194.22 and by proxy, 1194.21. It should only take a few minutes. It’s not as bad to read through as the W3C’s Web Content Accessibility Guidelines (WCAG). And, more importantly it’s not as comprehensive.
Once you get the highlights, WebAIM has provided a handy checklist. WebAIM is an open consortium that exists just for discussions such as this, similar to what OWASP is for Security. From the spec, (a) through (j) are reasonably straightforward. (k) needs to be understood, as “text only versions” seems to be a common accessibility misconception and isn’t necessary if all of the other items are taken care of.
Which seems to be a recurring theme when it comes to best practices. These things need to be thought about from the start, not thrown in last minute. So I think the solution for this is to spread information around. Not try to force this into existing projects, but bring them up as new projects / rewrites begin. It’s a lot to think about, I think the trick is to introduce the topics slowly but consistently into our culture until it becomes something we all know and just do without having to be told.