As one of the previous posters said, to add an application to the Dock, drag it in between two other application and then drop it and it should stay. If you can't get that to work, then launch the application, and once it is running, control-click it in the dock, and select "Keep in Dock".
For documents or folders, you have to get them to the RIGHT hand side of the dotted line near to the trash can. It's a little tricky but you should be able to get it to stay. You know you have it right, when the icons open up and make room for you to drop the object.
As far as making short cuts, you need to drag the original file to where you want the shirt cut to be, and BEFORE you drop, press the CMD AND OPTION keys. You should see the little shortcut arrow show up on the icon. Once you can see the arrow, THEN you can drop it. Don't drop it before than, or you will just move the file.
If you can't get it to work, then CTRL-CLICK on the original and select "Make Alias". Then move the shortcut to the location you want it to be...
Are you coming from a Windows background? I find that people who have used Windows for a long time, tend not to do much Dragging and Dropping, so it may take a little practice!