I have a folder with a lot of images. I want to have Photoshop resize all the images to 800px wide in an automated way so that I don't have to open each photo and manually set its size. Is there a way to have Photoshop perform batch processing on a set of photo?

Yes. ACTIONS will memorize the steps needed to resize your images. Read up on how to create an ACTION step by step. Open up and work only on the first image you wish to resize.

The general method is to activate the Actions menu, and under the flyout arrow, create a New Action and give it a name. Start the Action. Go through all the steps needed to resize the first image, including how you want to save it. To be safe, save it to a new directory. Stop the Action.

Open up the other items you wish to resize. Under File -> Automate -> Batch, select the newly named Action. Tell PhotoShop that the "source" is the opened files.

It works beautifully, BUT create a backup of your images beforehand to be safe, and practice first on something you can afford to lose.

You can also access this feature through Bridge. Browse to the images files, select the ones you want to work with, and select Tools > Photoshop > Batch. This just saves the step of opening up every image within Photoshop.

In the Batch dialog box, you can also choose to save the new images to a different folder and you can add extensions to the file name to help you distinguish between the originals and the ones you applied the action to. Just set the Destination to "Folder", otherwise you'll overwrite your originals.

In CS3, goto File > Scripts > Image Processor ...
Simple method to resize loads of images.
For more information see
Photoshop Resize Batch Images in a directory