In order to obtain U.S. Citizenship, you must follow all the rules and procedures set forth by the U.S. Citizenship and Immigration Services (USCIS), before AND AFTER the citizenship interview. There are rarely exceptions to this rule and many different things can go wrong after the interview if you are not careful.
What happens immediately after you finish the actual citizenship interview?
Usually you are notified of your result right away (unless there are any unusual problems with your case) and will receive a Form N-652 providing the results of the interview. This tells you if the application has been granted, continued, or denied.
If the application was granted, you will need to sign a certificate confirming your information. Please make sure you check over your information very well before signing, as this is what will probably go on your naturalization certificate. Sometimes the naturalization ceremony will occur right after the interview, but often a letter is sent out within a month or two telling you where and when the ceremony is taking place.
Be patient when waiting for the letter, also known as the "Notice for Oath Ceremony (Form N-445)". If you have not received it within 90 days from the date of your citizenship interview then you should contact your local USCIS office and have them resolve the issue.
Leaving the country after your citizenship interview.
I would recommend avoiding having to leave the country between the time of your citizenship interview and your oath, as you have to report this absence (and any other notable changes) on your Form N-445. However, if you must leave then please call your USCIS office to confirm that it will not cause any complications to your case. Usually you will still have your green card up until the day of your ceremony.
Leaving the country after your oath is a little different. While you can probably leave the country on your original "country of origin" passport, re-entering the states could potentially cause you some troubles, as U.S. Citizens are expected to leave and enter the U.S. with a U.S. Passport only.
If you cannot attend the ceremony.
If you cannot attend the Oath ceremony on the specified date, notify your local USCIS office as soon as possible and they will reschedule you. Do not "skip" it by any means! Only after the Oath ceremony do you become a U.S. Citizen.
Congratulations!