Where is the ventral brain stem located and what is its function?

There isn't really a ventral and dorsal brainstem, but there are ventral and dorsal sides to the brainstem. Its the same anatomical region of the brain, just looking at it from different angles (ventral is another way of saying anterior, and dorsal is posterior).

Most people refer to the medulla and the pons together as the 'brainstem'. The brainstem is located at the base of the skull, right above the point where the spinal cord attaches (called the foramen magnum). The pons is an important relay center for messages b/w the spinal cord and brain. It has several key nuclei, including the nuclei of some of the cranial nerves. The medulla also relays info and has nuclei, but it also has regions that govern arterial constriction/dilation, breathing, and heart rate, among other things. Functionally, its hard to describe the difference b/w the ventral and dorsal sides to the brainstem; the ventral side just has different nuclei and tracts than the dorsal side. Anatomically, from the ventral view you can see a lot more of the cranial nerves.