For the banana/yogurt I mix equal amounts of banana and plain yogurt in the blender, adding the yogurt after the banana has been thoroughly pureed.
The mango/carrot I do the same way, starting out with the carrot because it is a little more difficult to puree than the mango.
After everything has been thoroughly mixed, I pour the "smoothie" into ice cube trays and freeze. For larger dogs, you can use mini dixie cups too.