Image galleries are a favorite feature of many social networks, blogs and personal websites. So it's no surprise that many Drupal users want a solution to integrate images into the sites they are building. There are many ways to accomplish this using Drupal but I'm going to point out two that have worked well for me.

Basic

You can create a very good, basic image gallery by using the image module and taxonomy. When you add the image module a link will be added to your administration menu called image galleries. That link will allow you to define galleries that you can add your photos to. You will also see a new content type called image that allows you to upload images one at a time. You can add a description to each image and add it to a gallery that you have created. You can see an example of this basic type of gallery by going to http://learnbythedrop.com/image. The image module also provides settings that allow you to define image sizes so that you can have automatic creation of thumbnails and preview images.

I've kicked my basic image galleries up a notch by adding the very simple Lightbox2 module. Lightbox2 adds a script that allows images to be overlayed on the page when clicked. This adds a very slick effect that makes it easy for site visitors to browse your images. The Image Assist module which makes it easier to add gallery images to your posts is also very helpful.

Advanced

If you're looking for image gallery functionality with stronger features then I suggest checking out the Gallery module. Gallery is different from other Drupal modules because its main purpose is to integrate your Drupal install with another piece of software. The software that you're integrating with is the open source Gallery photo organizer, which needs to be installed on your web server before you add the Gallery drupal module. The process of combining Drupal and Gallery is a bit complicated. But once the integration is complete you get some serious features that allow you to create an excellent photo gallery for yourself or an entire community of people.

I have integrated Gallery on a private family site for myself that is powered by Drupal. I do not recommending getting started if you are in a rush. You will be most successful if you follow directions and take your time. Gallery is a system in itself and you'll want to spend time learning and exploring Galleries add on modules too. You can see a Drupal/Gallery integration in action over on the Drupal Gallery Demo Site.

Custom Gallery Creation

If you're looking for something that is truly custom then you always have the option of creating your own image publishing process by using a variety of modules. You can use Content Construction Kit (with ImageField) to create a special content type for adding images. You can use the Views module to handle the display and organization of uploaded images. The ImageCache module can take care of post-upload processing tasks like thumbnail creation. You can find a very helpful  custom image gallery recipe on Drupal.org. The post is titled Create an image gallery using only CCK and Views.

Flickr Integration

Flickr is a hugely popular image publishing service. So it's very possible that you may want to use Flickr to power the gallery on your Drupal site. There is a module called Flickr that eases integration and allows you to embed photosets and create photo blocks on your Drupal site.