The main section, above the census, is where you increase or decrease the number of kittens on a given job. You don't get fine-grained control over which kittens are doing which job, but you don't really need it; removing a kitten from a job using the [-] button always removes the kitten who is least skilled at it (of those working at that job right now), and adding a free kitten always adds the free kitten with the highest skill in it. As of 0.9.9.2, you can remove a specific kitten from their job when you unlock the Census, but assigning still always assigns the most-skilled kitten.
Note that your kittens can be skilled in more jobs than display, so you may not always be able to tell at a glance, but under most circumstances, your kittens shouldn't be changing jobs too often anyway.