The things you are carrying are listed in the Inventory window. The things you can do with them are listed in the Inventory menu. (Don't confuse the window with the menu!)
To do anything, you must first select an object from the Inventory window. Just point at the line you want, and click the mouse. (For example, to do something with the lantern, point at the line that says "a lantern" and click on it). The line will become highlighted. Then go up to the Inventory menu and select what you want to do. If the items in the menu are dim, then you've forgotten to select anything.
You can rearrange the things in the Inventory window by dragging them with the mouse: just point at something you want to move, press and hold the mouse button, move the mouse up or down to the new location, and let go. This is just for your convenience; it doesn't matter what order things are in in the Inventory window.
See the next Help section , called "Using Things", to learn more about what you can do with the stuff in your inventory.