I know this may sound stupid, but how do I delete photos so that I can keep only the best shots?

Hi Sue. What Operating System are you using (Mac or Windows)?

You said:  I am trying to delete a lot of my shots and can not find a delete key! 

If you are talking about photos that you have imported into the Elements Organizer, you can select the ones you want to delete and a blue checkmark will appear on them.  You can then use the Delete key on your keyboard; or go to the Edit menu and select Delete Selected Items from Catalog:

You will then be presented with an option to delete the photos from your hard drive.  If you do not accept this option, the images will only be deleted from your catalog. 

Note that when you import photos into the Organizer's catalog, you are only creating database references to the files that exist on your computer's hard drive.  If you imported the files from a camera or a memory card, the photos are first saved on your hard drive and registered in the catalog.  So, if you choose the option to delete from the hard drive, they will be deleted forever (unless you have backup copies or the copies are still on your camera's memory card).

You asked:  Are photos automatically saved after making edits?

No.  But if you are attempting to close an edited file without saving it, a message will pop up asking you if you want to save your work.

You asked:  Also, can I rename photos? 

The answer is yes.  But do not do that outside of Elements otherwise the Organizer will lose track of the photos you are renaming.  If you want to rename a file after editing it, you can do so in the Save or Save As dialog.  Depending on the nature of your edits, the dialog may offer to save the file as a PSD file.  If you want it saved as a jpeg file, you need to change the file format.  I also recommend that you save the file in the Organizer and ALSO save the file in a version set with the original.  If you do this, Elements will save your edited file in a stack with the original.  The edited file will appear on top of the stack but you can always go back to the original file.

I know I am throwing a lot of information at you, but it is best to give too much than too little in answer to your questions.  There are no stupid questions.  We are here to answer any questions you may have.