You can display normals as small blue lines in the 3D views. You can set the display size of normals in your preferences.
Additionally, there are some specific options for displaying normals that apply only to polygon meshes.
Instead of (or in addition to) displaying shading normals at the points, you can display the geometric normals in the centers of polygons.
You can control whether the normals are displayed for the entire selected object, or only for selected components.
Both of these options can be set on the Attributes tab of the Camera Visibility property editor:
To display the Camera Visibility property editor for a single 3D view, press Shift+S while the pointer is over that view. Alternatively, choose Visibility Options from the Show menu (eye icon).
To display the Camera Visibility property editor for all open 3D views, choose Display 
Visibility Options (All Cameras) from the main menu.
For a description of all the option that you can set in the Camera Visibility property editor, see Objects [Properties Reference].
In addition, some of these options can be toggled directly from the Show menu (eye icon) for a single 3D view, or from the
Display Attributes menu for all open views.
To display normals on selected objects in a 3D view
Click on a view's Show menu (eye icon) and choose Normals.
For other ways of setting this and other display options, see Displaying Types of Elements and Other Data [Viewing and Playback].
Changing the Display Size of Normals
You can change the display size of shading normals in the 3D views. This affects normals on NURBS surfaces as well as polygon meshes.
The size is controlled by the Normal Scaling parameter on the Component Display tab of your Display preferences. See Display Preferences [Preference Reference].
Displaying Shading versus Geometric Normals
There are two independent options for displaying normals on polygon meshes:
Normals displays the shading normals at vertex locations. These can be either auto or user normals, depending on whether user normals are defined on the object. This option also displays normals on NURBS surfaces.
Polygon Normals displays the geometric normals in the center of polygons. This option affects only polygon meshes. These are not the normals used for shading.
These options can be set on the Attributes tab of the Camera Visibility property editor, or directly from the Show menu (eye
icon) or Display Attributes menu.
Displaying Normals on Selected Objects or Selected Components
When displaying normals on selected polygon meshes, you can decide whether the normals are shown for the entire object or only for selected components. Open the Camera Visibility property editor and display the Attributes tab, then set For Selected Objects in the Show Normals box to the desired value:
Show On Whole Object always displays normals on the entire object.
Show On Selected Components displays normals only on the selected points or polygons, or the points and polygons adjacent to the selected edges.
Combo (depends on selection mode) displays normals on the entire object when an object selection filter is active, and on selected components when a component selection filter is active.
