Traditionally there will be photographers onboard your cruise ship. You will meet them first at embarkation when they will take a picture before you go onboard. From then on you will see them regularly at all the ship events and dinners, taking photographs of guests and possibly a video of the cruise experience.
Many passengers take advantage of their opportunity to have a portrait taken on the formal nights of the cruise (if applicable to your chosen cruise). Onboard, you will never have to purchase a photo if you're not happy with the way you look and you can even have the photo retaken.
Cruises are also great for getting family and group photos taken when you have a captive audience and it's otherwise impossible to get everyone together at home.
The results of their work are displayed in the Photo Gallery (usually near the Shops) where you can see how you look before you buy. If you don't like what you see there is usually a box in which you can put photographs you wish to see destroyed. Expect to pay around £5 per photograph for any you wish to buy with discounts for 3 or more.
If you have a traditional camera with film, don't worry about running out, the Photo Gallery will also be able to sell you film and also process your pictures whilst you're onboard, delivered to your cabin should you wish.