If I move a picture to a different album and delete it in the original album...it deletes both? How do I put a picture in a different album and delete it from the album it was in?

There is no "moving" of photos, nor are they copied. All you are doing is putting them in some semblance of organization, whether you use Albums or Folders. All Photos is all of the photos. They will always be there. They will also be in every other Album or Folder you put them in. None of them are copied.

You can Remove a photo from an album using the command in the Image menu or in the contextual menu or by pressing the "delete" key.

If you use cmd-delete, then it will delete the photo from the entire library.

ok but I have all my family photos in one huge pile and I want to make three folders, one for each of my offspring, so I select and drag the pics into the appropriate folder and it seems like all I'm doing is duplicating them..... I don't want them in the huge pile, I want them organized in the folders with names. What am I doing wrong? The old program iphoto was easier for me to understand