Preview saves file to desktop

Hi, and thanks for the welcome!

I can do a Save as, that's not a problem. Everything I look at in Preview is saved on my desktop and my desktop gets so full! JPGs, PDFs, etc. So even if I do a Save as to a different location, Then I get two copies of the file or picture or whatever saved to my computer. I want to eliminate the saving to my desktop.

My version of Preview does not have any preferences for saving anything. They're not on the Desktop before I open Preview.

Ok, I just deleted a pdf file I had, and did a secure empty trash. Then I went to a webpage with the pdf file I want to look at. When I click on the link for the pdf file, I get a window telling me I'm opening the file. I'm using FIrefox, guess I forgot to mention that. The popup box asks me what I want to do with the file. The only box I have clicked is "Open with ... Preview (default)"

The preferences box for Firefox for General has "Save file to ... " grayed out, and the option for "Always ask me where to save files" is selected.

It can't be Mail that's doing it; I've already got it in my preferences that downloads go to the "mail downloads" file.

Ok, I did that. And guess what, it doesn't work! It still saves the files to my desktop, and the folder I created and set the "Save files to" stays empty.