Within the new Image Collection, there are two ways to upload photos.
The first way is very similar to the method you may be accustomed to: clicking on/dragging images to the blue square.
The second way, and an easier method if you are looking to upload multiple images at once, is to click on the blue "Bulk Upload" button in the top right corner of the gallery.
When you select the Bulk Upload option, you will be redirected to another window to upload all of your files. The window will look like this:
Once all of the photos are finished uploading, you'll see them automatically load into the image collection.