deleting files only copies them over and over

I know other people have had problems deleting files but no one has really addressed how to get them deleted.  I have tried to clean up my pictures folder only to discover when I deleted them they only got copied.  Now instead of 100 pictures I have thousands of them.  In desperation I deleted the whole My Pictures folder and now I have gobs of shortcuts on my desktop that will not delete either.  What is the trick to get rid of unwanted files.  I remember now why my desktop has been gathering dust as I had to reformat last time to get rid of the mess but should not have to do this everytime.  I would love to start using my desktop instead of laptop for email and other programs but getting rid of useless pics is ridiculous.  It makes the  Apple computer more interesting all the time especially since no one at Dell seems to have a clue how to do this.