Most of the time you use a CharacterController for puppets (your player, enemies, npc, ...) for other objects that need to interact use Colliders. Add a CharacterController using Component menu. Make sure the Controller is not already through the collider of the terrain (place the char a bit above the terrain!). If still falling through, check if terrain has collider set correct (look in last tab of inspector if Terrain when terrain is selected), the last component should be Terrain Collider. The checkbox isTrigger should be OFF!

If it still doesn't work, create a GameObject -> Create Other -> Cube and place it under your character. If char falls through cube, it's something missing in your character, not the terrain. Select your character and see if there's really a Character Controller component attached, the green capsule you should see on screen when char is selected should match the char size more or less. Twiddle with values, make sure Skin Width isn't too small, start with 0.1 if not sure. Mess with center and size until capsule matches your char, if still falling through, reply and we'll look further :-)

Have You checked your character is not through the terrain? maybe that's the problem.