There are lots of questions revolving round the passport issue right now. To make this a simple issue lets just say that yes you need a passport and so does your child, regardless of age.
International security has become a huge issue and requires that anyone traveling outside of the U.S. have a passport to get back into the country; other countries require a passport for entrance. It’s best to be prepared for the unexpected when traveling. For example, if you miss the boat after an on shore excursion you may need to fly out of that country to get to the next port, or to get home. Or perhaps you miss the boat at the beginning cruise port and need to fly out of the U.S. to the next port of call to get on the ship. So, since you never know what might happen get yourself and anyone who will be traveling with you a passport.
Okay, so you need a passport, how do you get one? Basically you get a passport picture, get your identification and proof of citizenship together, fill out the application, submit the application, submit the fees and wait. Simple right? Kind of. The first time I got my passport I ended up going to the post office three times because my picture wasn’t right and then the application wasn’t exactly right. Save your self some time and make sure you get everything in order BEFORE standing online at the post office.
The U.S. Department of State Passport Page is the best place to get up to date applications and information on getting yourself a passport, renewing your passport, replacing a lost passport, and obtaining a passport for your child.
Some things to keep in mind (and please verify on the Passport Page in case I forgot something):
- DO NOT SIGN YOUR APPLICATION until you are instructed to do so by the passport acceptance agent.
- BOTH PARENTS MUST SIGN A MINOR’S PASSPORT APPLICATION.
- The passport applicant must appear in person (regardless of age) when applying for the first passport or replacing a misplaced or damaged passport.
- Passports generally take 6 to 8 weeks to process and be mailed back; you can expedite that for $60 + overnight shipping costs in addition to the normal cost.
- Currently the cost of a passport is $97 for anyone 16 and older, and $82 for children under 16.
- You will need to submit your certified birth certificate, if you don’t have one there are other options listed on the passport site.
- You will need proof of identity (like a drivers license or millitary ID)
- For minors without ID parents must provide proof of identity and vouch for the child.
- You will need to have 2 passport photos that meet the photo requirements (I’ll post those below).
- You will need to provide a Social Security Number.
These are basic application requirements but there are a whole slew of alternate options that will serve in place of the standard birth certificate and drivers license options. These will be listed in the document How To Apply For A Passport.
Also, the photo requirements are as follows:
- 2×2 inches in size
- Identical
- Taken within the past 6 months, showing current appearance
- Color
- Full face, front view with a plain white or off-white background
- Between 1 inch and 1 3/8 inches from the bottom of the chin to the top of the head
- Taken in normal street attire
- Uniforms should not be worn in photographs except religious attire that is worn daily.
- Do not wear a hat or headgear that obscures the hair or hairline.
- If you normally wear prescription glasses, a hearing device, wig or similar articles, they should be worn for your picture.
- Dark glasses or nonprescription glasses with tinted lenses are not acceptable unless you need them for medical reasons. A medical certificate may be required.
There are a lot of places that offer passport photos. I went to CVS to get mine and ended up having spend more money to get new photos made since the CVS cashier I got that day didn’t understand the passport photo requirements. My suggestion is to get your picture from a place that understands the requirements and knows how to produce a picture with them. Kinko’s worked well for me, and many U.S. Post Office locations offer passport photo service as well. The little photo booths in the mall are not going to work. 
You can use this link to find the Passport Acceptance Agency closest to you.
So now you have an idea of what to do and where to find more information, get this process started early you will be happy you did. Have fun!