I remember my dad getting me one when I was a boy in the 1980s, but haven't really seen them around since.
After doing some research, here is a really good comprehensive website dedicated to them:
On this website it states that there is no 'clear answer' as to how to make your own baking soda submarine. Well, now with 3d printing technology, the answer is simple - model and print it!
Date Made: June 2013
Approx Cost: (Cost of printing?)
Approx Time: 3 hours modelling (plus printing time)
(Note: image taken from http://jamesrising.com/2011/04/23/what-wine-goes-with-fruit-loops/ under fair usage)
Step 1: How To Operate
Next You fill the small compartment of the submarine with baking powder and put the lid back on. These toys use baking powder not baking soda. (I presume it is the same terminology in the USA?)
Then launch your submarine - place it in the water and give it a quick shake, ensuring that the lid doesnt come off. The submarine will sink. After a short amount of time it will float and then it will repeatedly sink and float.
Here is a video showing you one working:
(Note: image taken from http://www.inlieuofpreschool.com/submarine-science-for-kids/ under fair usage)