In this photograph I have been told, that the eyes are looking like "black pools", which I do realize now.
What should be an ideal placement of ONE artificial light source (lamp/flash), so that eyes have a sparkle in "portrait" shots?
If this depends on certain conditions please list down them too.
To get a "catchlight", which is the term for the reflection of a light in the eyes, you'll need to put a light somewhere that the eye reflects. (Sorry if that seems obvious.) Essentially, this means someplace that the eyes can see.
If your subject is facing the camera, the obvious place for a light is near the camera -- this will create a reflection near the center of the eye. A popular way to do this in portrait and fashion photography is with a ring light -- a light that wraps around the lens. This creates a circular catchlight that will wrap around the subject's pupils if they look directly into the lens. Another way to do this is with a catch card or bounce card, as Gapton points out, or with the on-camera flash. In this case, I think a bounce card will be too high, and be shadowed by your subject's eyelids.
Likewise, a light placed above and to the right of the camera will create a catchlight above and to the right of the center of the eye.
In your case, since your subject is looking down and to the left, you'll probably want to place a light at low camera left. You could also place the light near the camera, and get a catchlight to the right of the pupil. If you place it to the right of your camera, your subject's left (camera right) eye might catch it, but on the outside edge. Chances are, the nose would shadow the other eye, preventing a catchlight from appearing.
Adding a light to create a catchlight will affect the mood of your photograph -- for one, the catchlight "puts a sparkle in your eye", literally speaking, and will convey that emotion onto your subject. Second, the light that creates the catchlight will also light the rest of the face, and may take away the shadow that makes the photograph seem somber and pensive.
If you are using an External Flash, it probably already comes with a "catch light" card.
A "Catch Light" is the said sparkle in the eye. The light source is usually placed high, above the photographer's shoulder, sometimes to the left, sometimes to the right. It doesn't really matter which side you put it on, but some photographers do prefer it to be at an angle instead of being "straight above", since this will produce a catch light that is at the 12 o'clock position of the model's eye.
If you are not using a flash, like this photo suggests, it may be more tricky since you will inevitably shine some light on the subject's face no matter what you use.
For this photo you can consider placing the light source to the right of the frame, so that it will no destroy the shadow you are trying to create on the left side of the frame.
