Select "Path" mode from the toolbar. The editor options dialog will open that additionally prompts for basic path parameters, such as width and extension scheme. When a path is being drawn, it will receive the settings entered into this dialog. The path properties can be changed, while the path is being drawn. If the option page has been closed unintentionally, it can be reopened with the F3 shortcut.
To actually draw a path, choose a layer from the layer panel in which to create a new path. Left click at the first vertex, move the mouse to the second vertex, click to place this one and continue to the last vertex. Double-click at the last vertex to finish the path. Press the ESC key to cancel the operation. Use the backspace key to remove the current segment and go back to the previous segment.
For paths, as for polygons, the segments created are subject to certain direction restrictions as imposed by the connection angle constraints. See Basic Editor Options for a detailed description of the modes. Use the "editor options" dialog (F3 shortcut) to change the mode, also during editing.
Paths are often used for wires. KLayout can be configured to provide vias that allow switching from one layer to another and place a via between the layers where the paths overlap. Before you can use the via feature, KLayout has to be equipped with via definitions. Vias are basically PCells which need to support a specific set of parameters. Via PCells need to expose a number of descriptors to define the options supported by a particular PCell (e.g. the layers which are connected or the type of via if multiple flavors are available). This scheme allows for a lot of flexibility, but needs some coding skills. In the macro IDE, a code sample is provided which implements two simple vias for a three-layer metal stack. For more details see PCellDeclaration, method "via_types" and ViaType.