In photoshop, everytime I choose: File / Scripts / Export Layers to Files... It exports each layer as a file just fine, but it puts a series of numbers and 2 hyphens like this "_0000_" in front of each filename. I made sure the "File Name Prefix" field was blank. Any ideas?

That's probably the default if you don't give it a prefix. It's got to name all the separate layers somehow. Try putting in a prefix and see what you get.

If I put a prefix say "01" then it comes out "01_0000_layername.jpg", "01_0001_layername.jpg", "01_0002_layername.jpg" and so on...

What do you want it to do?

I just want it to name the file the same as the layer name without any numbers. Like this "layername.jpg"

This is a suggested work-around.

Once you've exported the Layers to Files..., - set up a Photoshop Action to remove the prefix. Once you've created the Action, you can then process the entire folder, and save the files without the prefix to a separate destination folder.