Scaled images are generated at the time they are uploaded, not when inserted.
You can choose the sizes that WordPress automatically generates for images that are uploaded in your Dashboard Settings under Settings > Media.
Once an image has been inserted using Add Media, you can click the image and then click the edit image icon that appears in the top left of the image. Go to the Advanced tab, and you can set a new size for the image just for that post.
A new image is not created for the individual post, but instead an <img /> element is inserted with the width and height specified.