1. Hold right mouse while moving#

You must hold the right mouse button to use W, S, A, and D navigation to fly through the scene.

2. Set the camera speed multiplier to a reasonable value#

Make sure the camera speed is set to a reasonable multiplier like 1.

You can change this setting via the camera dropdown in the View Options toolbar overlay, which is anchored to the top right of the Scene view by default.
Alternatively, you can use the scroll wheel while holding the right mouse button in the Scene view to change the speed.

3. Set the camera to Perspective#

Disable the 2D toggle in the View Options toolbar overlay.

Click the center of the Scene gizmo or the label below the gizmo to toggle between Perspective and Orthographic views. Change it to Perspective.

I can't find the Scene gizmo.

4. Unlock the camera's perspective#

Make sure the Scene gizmo is not locked (the small icon at the top right of the gizmo).

5. Reset the Scene view window#

Reset the Scene view window or the editor layout.

6. Check for errors and warnings#

Open the Console window (WindowGeneralConsole, CtrlShiftC) and address any errors.
If errors or warnings are constantly printing they may be related to the Scene view.

Take extra care ensuring that logs are not disabled using the toggles in the top right of the window.

7. Restart Unity#

Close and reopen Unity.