[caption] 's Yet again

Ok, I’m trying to write a plugin and I’m confused. I’ve read through the Codex and got even more confused. And other forums made it worse. Here’s my problem.

I have $content. Which may or may not have a [caption] shortcode in it, as inserted by the TinyMCE when placing media. As long as I put that $content into a TinyMCE, I see the captions formatted properly. When I try to display that $content in say a table, the [caption] isn’t converted to HTML

Do I need a filter, a hook, a new shortcode… I dunno. I’m using a boilerplate to create this plugin so do I add this filter, hook, whatever, and it’s accompanying function into the ‘construct’ method or does it go into my menu?

Do I need an apply_filter on the $content? If so, where do I put that???

All I want is for the images to have their normal captions. I wouldn’t have thot it this difficult and confusing.