To snap an object to another object’s surface when moving, a common set up in Blender is to enable the relevant snap options:
To quickly switch on these settings, an option is provided in the menu that allows you to toggle these settings on and off:
In the viewport, right-click and select the Conform Object context menu.
Select the Toggle Surface Snapping option.
This will automatically enable snapping options so that you can align the object to the surface quickly.