You can use either a stand blender or a stick/immersion blender for this recipe, which will make your life a lot easier than trying to make it without.
However, if you insist on mixing this by hand then follow the steps below and use overripe bananas which will be easier to break down than those which are just ripe.
1. Place the banana into a bowl and use a whisk to mash it up into a paste.
2. Add the ice cream into a mason jar and place in the microwave for around 15-20 seconds, until just starting to soften.
3. Add the banana and milk to the jar and seal with a lid. Shake vigorously until all the ingredients have combined.
If you don't have a blender, then consider investing in one. They are pretty inexpensive and you will get a lot of use out of it over the years!