To help with focus, a person should look towards the Heavens before beginning
Shemoneh Esrei and this can be done at intervals during the prayer if necessary. But for the bulk of the
tefilla a person should keep his eyes down, and according to the Zohar they must be kept closed. Someone who is not careful to keep his eyes closed when
davening will not merit to see the Shechina upon his demise. There is an opinion that the Zohar permits a person to keep his eyes open if he looks down the whole time. The preferred method is to keep one's eyes closed, because that prevents people from looking around.
Davening from a
siddur with open eyes is permissible according to all opinions.
סימן צה, סעיף ב, ס"ק ד-ה, וביה"ל ד"ה צריך; ביאורים ומוספים דרשו, 11)