This upload process refers to all themes developed after July 2013 (in which images are uploaded via the WordPress Media Uploader).
To add add images to your portfolio post, click the "Add Media" button at the top left of the default portfolio post editor. After clicking this button you will see options to either drag and drop, or upload via a file editor. Pick whichever one suits your needs and upload your images. Do not hit "Insert into Post", simply close the uploader and update/publish your post.
By clicking "Insert into Post" you will add the in area straight into the content field of your post (not the intended area). WordPress saves your images via auto-save.
You can check the images uploaded to your specific post by selecting "Uploaded to this post" in the select field above the uploader.
From the Media Uploader, you may also rearrange your images. Simply drag and drop the grid layout (of the images attached to your specific post) and reorder them as needed. Then close out of the window - WordPress will auto-save your edits.