I'm trying to create a new icon for an item.

I followed this little guide.

http://cs.elderscrolls.com/constwiki/index.php/Paintshop_Pro:_Creating_Inventory_Icons

I moved the file into the "textures" folder because I've seen it look there for stuff frequently so I thought I'd toss it in there. I went to the item in the construction set, opened it's edit box, and clicked the rectangular box on the bottom that is to the left of the icon slot. I then selected the dds file and a little window popped up that said "Invalid Directory." That is all it said. So I moved it to the "data" folder because that's where it first brought me to. Same thing.

Where do I need to move it for it to accept it?

The item I'm making an icon for is an apparatus (if that in any way affects where I should place the file.)

Icons are very particular about file paths. Generally speaking, you want all of your icon files to be in the same directory as default Vanilla icons or a subdirectory within it. In this case, Data\Textures\Menus\Icons\Clutter. Note that, ideally, you should have an icon located in the Menus50 and Menus80 directories as well for systems with lower resolution.