Please note you can only use the snap function if you have a pre-existing feature in a project. You cannot snap to something only shown on the base map or data layers.
Ensure that the snap function is active by clicking on the icon, yellow is active white is inactive.
Select the feature on your map that you want to draw a snapped feature to then choose your drawing tool.
Move your cursor to your starting point and you will see that it is magnetised to the edge of the feature. single click to start drawing your feature.
Move your cursor around the feature and it will snap to the edge. Double click to finish and click on finish.