What's a good way to find the ground normal?

You could cast a ray in the -transform.up direction or in the Vector3.down direction, as @whydoidoit said. Vector3.down gives the normal of the surface below the character position, while -transform.up returns the normal under the character feet. The raycast range may be a little longer than the distance from the character pivot to its feet in order to compensate for inclined surfaces. You must decide what to do when the ground is out of the raycast range: you can keep the last surface normal or assume the world up direction (Vector3.up).
This is a simple code to find the normal under the character feet; if no ground is hit, the last normal is kept:

 private var distToGround: float;
 private var normal: Vector3 = Vector3.up;
 
 function Start(){
   distToGround = collider.bounds.extents.y - collider.center.y;
 }
 
 function Update(){
   // assume a range = distToGround + 0.2
   if (Physics.Raycast(transform.position, -transform.up, hit, distToGround + 0.2)){
     normal = hit.normal;
   }
 }

If you want to use the ground normal to make a character that aligns to the ground, take a look at the question Orient vehicle to ground normal. If you want a character that walks on any surface, take a look at the question Basic Movement. Walking on Walls.