If you want to promote your work as art, and yourself as an artist, then you probably want some sort of creative gallery rather than just a series of images. This isn't going to be a simple task, and as much effort will be required in the design concept as in actually coding the pages. Some photographers hire talented web designers to help out with this since it can be a complex process involving skills with programs like Macromedia Flash as well as a familiarity with HTML and page design using style sheets (CSS files).
Since complex gallery design is more the subject for a book than a web page, I'll concentrate here more on the type of gallery a photographers might chose simply to display examples of their work, or to present images they hope might sell as stock images.
My gallery pages were created using Jalbum, which is a freeware package. It's not hard to use, but it's not totally trivial either, especially if you want to modify any of the "canned" themes it comes with. If you want to modify the themes, you'll need to know some HTML and learn some features of the Jalbum scripting language. So although it's a very powerful package, it might not be the best choice for absolute web beginners if you want something customized. However there are a lot of design layouts already written for JAlbum ("Skins") and if one of them meets your needs, you're all set.
Webpicture Creator is a very useful freeware thumbnail gallery generator. If you don't want to see HTML, you don't have to. However using a few HTML commands and templates you can create a wide range of gallery styles. If you like tinkering under the hood a little bit, this might be an excellent program to check out. Again this is freeware, at at least donationware (if you use it a lot, the author requests you make a small donation). Another freeware program is Lightbox JS. Lightbox JS is a very small program with a very simple interface, yet it produces a very nice image gallery. It's very fast too. You can see an example I created in under 1 minute here - Lightbox JS sample gallery. Another simple freeware (or "donationware") program which doesn't need a database is PHP Album. Also be sure to check out Picassa, which although it's much more than a gallery generator, can nevertheless produce a range image galleries which can be uploaded to your website, and Simpleviewer, a flash based gallery generator which is easy to use and generates nice looking galleries.
If you want a higher end database driven program that can do a lot, you can look at Coppermine, 4Images and Gallery. These applications need some smarts to install on a webserver (and the webserver has to support the requirements of the program), but it could be a good way to go. If statements like "Coppermine is a multi-purpose fully-featured and integrated web picture gallery script written in PHP using GD or ImageMagick lib with a MySQL backend" leave you scratching your head, this probably isn't the package for you if you don't have help around.......however some website hosting packages include a feature called "Fantastico", which is an installer for a number of open source programs including Coppermine, 4Images and Gallery. Installation is then simple and all the server configuration and script installation is done for you. Again HOSTMONSTER has Fantastico which makes the installation of these powerful gallery programs very easy.