I want to create a widget for my theme that will let me upload an image to WP and crop it to a certain size. Can anyone point me to the codex page or a tutorial on how to a bare bone implementation of it?
This tutorial explains basic use of WordPress media uploader.
To add image sizes use
<?php add_image_size( $name, $width, $height, $crop ); ?>
Read more on this at Codex