Files that contain programs for the Mac are usually downloaded as .dmg (Disk Image File) or .zip (Compressed File) files. (.exe files are for Windows machines and, for the sake of this post, should be ignored entirely)
Once you have downloaded your file, your next task is to locate it. By default, if you are using Safari as your browser, the file "should" be in the Downloads folder. (This is a setting that you can make inside Safari Preferences if your downloaded files do not go to the Downloads folder)
Double click the .dmg or .zip file.
If the file is a .zip, then the system will expand the file and create another file, usually with the same name, in the same place. This is the file that actually contains the program. Double click this file and follow any instructions.
If the file is a .dmg, double click it. Follow any instructions.
You will find that, usually, when you double click a .dmg file, an icon that looks like a hard disk appears on the desktop. Usually, another window opens with the actual contents of that image but not always. Double clicking the icon will open it for you.
More to follow if necessary.
This is,of course, a simple thing, but I am more simple still. Have program downloaded on my new macbook pro. Some I click on in the download file and they start right up. Of coarse, the ones I really want do not. Would really appreciate some help.