I would only like to show watermarks to guests (anyone that isn't logged in) but let logged-in users see and download watermark-free images. Seeing the watermark on the image page but downloading it without one would be fine too. Is there an option for this?

To do this you will have to have your theme use different function calls for logged-in users versus the general public since the watermark is permanent in the cached image.

You can use printCustomSizedImage() to show the image with or without the watermark--that is a parameter to the function.

I'm using the default theme, dark. How would I implement this, and is there a doc page for the function?

There is: http://www.zenphoto.org/documentation/functions/_template-functions.php.html#functionprintCustomSizedImage

Okay so now I have it displaying images without a watermark, but they are very large. What is the format of the "size" parameter? I tried $size = 595 assuming it was the width in pixels, but it didn't work.

"Size" is in pixel. If it is the width or height depends on your image option settings regarding "longest side". If it didn't work you maybe did not set the parameters correctly.
http://www.zenphoto.org/news/how-to-read-the-zenphoto-functions-guide

Okay, the size works now, but the watermark show up now too. What do I need to put in the $effects parameter to hide it?

$thumbStandin is the one and must be set to false. That means the image is treatened as a "thumb" and the only difference between a thumb and a sized image is that thumbs don't have watermarks.

That works! Now how can I also hide it for logged in users on the full image page?

full-image.php isn't there.

There is no full-image page on theme level and it is only used for protected images. Use the image functions for it.
http://www.zenphoto.org/documentation/functions/_template-functions.php.html#functiongetUnprotectedImageURL
http://www.zenphoto.org/documentation/functions/_template-functions.php.html#functiongetProtectedImageURL

Add a check using if(zp_loggedin()) { … } else { … }

It works perfectly now!

I have it set up so that logged in users see and download (no more full-image.php... I have so it downloads directly) a watermark-free image while guests see and download a watermarked image.

Thank you!

Hah! It was messed up by the ``