Your monsters will not do anything unless you tell them to. No one said it was going to be easy.

Eating and sleeping are not jobs and monsters will take care of themselves on their own as long as you provide them with food and beds to sleep in.

The job menu lets you assign jobs to your monsters.
All monsters can perform all jobs, but some monsters are better at some jobs than others: check their star rating for each job.

To assign a job, click on the star rating. The monster will automatically start doing the job - if they are in the middle of another job, it might take a few minutes for them to finish what they are doing first.

To unassign (or cancel) a job, click on the star rating again. The monster will automatically stop the job.
If the monster has another job lined up (see prioritizing jobs) they will start on their next job.
If the monster doesn't have another job lined up they will become 'idle' and will remain so until you assign them a job. Idle monsters still need to eat and sleep, and are still at risk of being attacked.

Jobs can be prioritized so monsters do more important jobs first. It is up to you to decide what job is more important.
Priorities can be changed at any time, and you may find that a job that was once a low priority becomes the highest priority.
Use the arrows in the job window to give jobs a higher priority (to the left) or a lower priority (to the right). High priority jobs will be done first, then the monster will move to the next job to the right.
If there is no more job for the monster to do, they will become idle. Idle monsters still need to eat and sleep, and are still at risk of being attacked.

OR

There will be times when it will be useful for your monsters to stop performing a job for a little while. You can stop a job for a single monster, or you can stop all the jobs for all the monsters.
To stop a job for a single monster, click on the icon at the end of their list of jobs. Click on the hand again to get the monster working again.
To stop the jobs for all the monsters, click on the icon at the bottom of the window. Click on the icon again to get the monsters working again.