The Halacha of "Amira Le’nochri" forbids instructing a gentile on Shabbat to perform Melacha – activities that are forbidden for a Jew to perform on Shabbat.
With regard to "Remiza" – hinting to a gentile to perform Melacha, as opposed to a direct request – Halacha distinguishes between two different kinds of hints. If the hint is expressed in the form of an instruction, then one may not hint to a non-Jew in this fashion on Shabbat. The Gemara gives an example of a person who wants a gentile to extinguish a wick, and says metaphorically, "Clean your nose." Even though the request was made through an indirect allusion, it is nevertheless forbidden since it was formulated as an instruction. It is permissible, however, to hint to a gentile by making an observation, without expressing a command or a request. For example, if a person received an important letter on Shabbat which he wishes to read, he may say to a non-Jew, "I can’t read this letter because it is forbidden to open envelopes on Saturday." The non-Jew will then understand on his own that he should open the envelope for the Jew.
Similarly, if a person wishes to read in a dimly-lit room on Shabbat, he may say to a non-Jew, "There isn’t enough light here," so that the non-Jew will turn on the light. It must be noted, however, that this applies only if there was some light in the room but the person wanted additional light to allow for more comfortable reading. This occasionally happens on Shabbat afternoon, when sunlight enters through the window but a person wants additional light. This could also happen on Friday night, if some lights are turned on but a person wants the others turned on, as well. In such cases, one may hint to the gentile to turn on the desired lights, in the manner described above. However, if a room is entirely dark, one may not have a gentile turn the lights on for him even if he asks indirectly, through a hint.
Summary: Although one may not ask a gentile to perform for him on Shabbat activities that are forbidden for a Jew to perform, one may hint to a gentile by simply observing the situation, such as by stating, "There is not enough light here." However, if a room is completely dark, one may not even hint to a gentile to turn the lights on.
