Puppy's menu can be opened in 2 ways: through the "Menu" button on the panel's left and by right-clicking the desktop.
When the desktop is empty an few windows are opened, it is more convenient to open it by right-clicking the desktop, because most if its area is free. However, when many windows are open, it is hard to find where to right-click it, so the button is more useful in such cases.
The menu is sorted by application categories. For instance, applications that deal with graphics are contained inside the "Graphic" sub-menu and internet-related applications can be found under "Internet".
To start an application, enter its sub-menu by moving your mouse on it, then, click the application's name or icon once to start it.