(The majority of the following information was supplied by an official cache approver)
The vast majority of caches are reviewed between 0 and 48 hours after submission. However, there are many reasons why there might be a delay in the approval of your cache. If you ever have a question about the process, send an email to your local approver. If you don't know who your local approver is, just ask in the forums here.
Here are a few things that you can do to speed up the review and approval process:
1) Provide plenty of information when submitting your cache.
Remember that too much information is always better than not enough. Use the "Note to the Reviewer" section of the submission form to give specific information to the approver about the cache (coordinates for multistage puzzles, final coordinates for puzzle or offset caches, etc...)
2) Review your cache location for nearby problem areas.
Look at your cache location on a map. If you see things like railroad tracks or an airport nearby, chances are that your approver will ask about it. Let the approver know about any special or unusual circumstances regarding the location of your cache.
3) Review your cache location for nearby caches.
While you're checking the cache location, you should also make sure that your cache is at least 528 feet (0.1 mile) from the nearest cache. This is one of the most common reasons for a delay in getting a cache approved.
4) If you need to communicate with the approver, use email.
When an approver posts a note to your cache page, you will receive a notification via email. Just remember, however, that when YOU post a note, the approver is not notified. If you wish the approver to see your comments, you should send it via email.
For more information about the guidelines for placing caches, visit Geocaching.com's Cache Listing Requirements/Guidelines