Step 1 - Select the board you want to edit

First you need to go to the board that you would like to edit by going to Settings > Boards and then pressing on the board that you would like to work on.

Step 2 - Drag and drop your cards in the desired order

All you have to do is to tap on one of the image thumbnails (cards) and keep your finger pressed for a second.  Then start to drag the thumbnail into the desired place.  Cards are organized from top to bottom and from left to right.  So the first 4 items appear in the first row from 1 to 4.