It really depends on where you're downloading from.
With Big Fish, you download a small downloader file and run it, which starts up the Big Fish Game Manager, which downloads and activates your game.
GOG gives you a link, or to a picture of your game on a virtual bookshelf -- click the picture of the game and you'll see a collection of files you can download individually. Or you can use their download manager, but I've always downloaded the individual files.
Some places will send you an email with a link to the file or files you need to download. An activation key may be included in either the same or a different email.
It all depends on where you're downloading from.