I'm pretty sure they are strapped to your arm so the point is down.  I've always seen them used that way.  Meaning the flat top is parallel with your forearm. 

Having used a variety of shields in combat, how they are fastened or held can vary quite a bit. For the typical "heater", or triangular shield, the arm is usually not parallel, but more diagonal, with the hand pointed to the top right(backside) of the shield, and as Lord Xia notes, at rest the shield would be sideways, or even top down, point up. Still, most fighters will go with what works best for them, some will have the arm perpendicular, secured down the center of the shield. Bucklers and targes are typically strapped to the forearm, or simply grasped, usually by a raised dowel or a strap. Kite and tower shields are carried much the same as a heater, for those with the strength to bear them.

A properly fitted heater will see the point just above the wielder's knee, with the top parallel to his shoulders, when in a fighting stance.

Kite shield:

Buckler:

Source: http://www.yeoldegaffers.com/project_shield.asp

No worries. I've been involved in medieval re-creation for several decades; tend to pick up a tidbit of knowledge or two, along with the broken bones, bruises and tumors.

Side note, the term "heater" is often used in medieval based fiction, even in "historical" novels. Unfortunately the term dinna come into usage until the Victorian era, and was coined due to the similar shape of the shield.... to the clothes iron.

I always hated that my bard got the shield proficiency but couldn't cast spells with a shield equipped...oh, I am going on a weird tangent now...

Bard instrument:  one-man band!