To make a job inactive, find the job on the Jobs tab and click the Make Inactive button.
You will be given the option to Make Inactive (you will not receive new applicants), or to Make Passive (you will accept resumes for future openings). Both options take the job down from the job boards, but 'Make Passive' will leave the job on your Careers Page.
Be sure to complete the action by clicking the Make Inactive button once you have selected your option.
If you decide to make a job inactive (rather than passive), you will be asked whether you want to keep the applicants to that job active or de-activate them. De-activating them will remove them from your default visible applicants screen. However, you can always make inactive applicants active to work with them at a later time. You can view inactive applicants by changing your applicant filtering options: How do I use the sort and filter options on the applicants page?