okay george, I'll try to help you
1-download yahoo messenger. save the .dmg file to your desktop or downloads, wherever your downloaded files go. Double click on it after it has downloaded and it should open up. (ah, I see-i checked out the youtube video on how to install it). then read the terms and conditions, click on agree, then drag the app (the smiley face) to the Applications folder (the square, as you call it), then it should copy it to the Applications folder. Then right or control click on the open yahoo messenger .dmg thing, and choose Eject, which should eject it into the trash. You are done installing Yahoo Messenger. click your hard drive icon on the right top of your screen and move to the Applications folder. Yahoo Messenger should be there. If you need quick access to it, or use it a lot, you can drag a copy to the dock....
Why are things so difficult? it's good to be curious, george. Might I suggest booking some time at the Apple store, or if you can afford to, pay for some one-to-one training
Using the Mac isn't difficult, but it does take some practise and getting used to