Accessing WordPress's image upload functionality from a plugin

Does anyone know of an elegant way for plugins to hook into WordPress’s image upload functionality from their settings pages?

I’m building a gallery plugin at the moment and I’m trying to use as much of the underlying WordPress functionality as possible to keep it simple and easy to maintain. This seems to be a sticking point though.

Basically I want to add an ‘insert image’ button on the plugin’s settings page that launches the familiar image dialogue box from the edit post screen. It should let the user upload a new image from their computer or select an existing image from their media library – exactly as it works when you’re adding an image to a post. If the user uploads an image it should process the uploaded file as normal, producing the thumbnail versions and adding an entry for the image in the media library. Either way, I’d like it to return the attachment ID of the selected or newly added image for use in the gallery code.

All this functionality is built into WordPress already so it feels like there should be an easy way to do this – but if there is, I can’t find it. The solutions I’ve found so far have been hacky and look like they’d be messy to maintain.

Does anybody have any suggestions on how to go about this? I’m sure it’s a feature a lot of plugin and theme authors would like to make use of, so if I can get it working I’ll write up a full tutorial and post it here.