might I ask the reason for saving as gif? Unless it's for simple animations, there are better formats. Gif images have a limited colour palette (256 colours tops I believe) If it's photographic, go with jpg or png. Gif is only best for small, fairly simple animations and transparency.
If you just want to save something as a gif, Pulse-8's suggestion would be one of the easiest, and wouldn't require additional software. However, if you want the gif optimised for animation, Adobe Imageready could be the way to go. It may be bundled with Photoshop Elements. I know it's bundled with Photoshop, but I'm not certain if it also comes with Elements. If it does, you're in luck.
Now, if you want something with transparency (as the gif format offers you) then PNG is an alternative. It offers better transparency options, much better colours and reasonable file sizes for small images.
From photoshop (and photoshop elements) choose File>Save for web. Here you'll find all the options you'll need. Select the format and the options. It will give you a preview of the output file. Hit save, select file name and destination and you're done.
If you do want animation, that's slightly more advanced, and better left to Imageready.