Just to expand on DeltaMac's solution: there are two distinct sections of the Dock, visually separated by a divider.
The left-hand side of the Dock only accepts applications. This means that you can drag-and-drop individual applications to that part of the Dock; for example, if you wanted Microsoft Word application in your dock, you would locate the Microsoft Word application in your Applications directory, then drag-and-drop the Microsoft Word application to the Dock on the left-hand side of the divider.
The right-hand side of the Dock only holds documents and folders (not applications), and, like DeltaMac said, also includes the trash can. If you wish to have your Applications folder appear there, then you would locate your Applications folder (by opening up a Finder window, navigating to your hard drive, then locating the Applications folder), then drag-and-drop the folder onto the right-hand side of the Dock.
Once the folder is there, you can right-click on the folder in the Dock to bring up a menu of display options: these options will determine how, when you click on the folder, the icons within the folder are displayed. Some options are in a "fan"-type icon list (which I don't much prefer), or other options, which you can play around with and choose the best one to your liking.
You can do this with more than just the Applications folder -- if, say, you wanted quick Dock access to your Documents folder, you could drag-and-drop your Documents folder down there on the right-hand side to have quick access to the contents of that folder.