Gemara

17b (Mishnah - Beis Shamai): On Erev Shabbos, one may not soak dye or ingredients [for dye] unless it will get soaked before Shabbos;

Beis Hillel permit [in any case].

18a - Question: Which Tana holds that putting water into dye is like soaking it? (Since one is liable for doing so on Shabbos, Beis Shamai forbid causing it to happen on Shabbos.)

Answer (Rav Yosef): It is Rebbi:

(Beraisa - Rebbi): If Reuven put flour [into a trough] and Shimon put water, Shimon is liable [for kneading];

R. Yosi b'Rebbi Yehudah exempts, unless he kneaded.

Question (Abaye): Perhaps R. Yosi exempts only for flour, which must be kneaded, but he is Mechayev for dye, for it suffices to add water!

75a (Shmuel): One liable for Shechitah for killing;

(Rav): He is liable even for dying.

Rav: He wants the place of Shechitah to be bloodstained, so people will see [that it was slaughtered today] and come to buy.

139b (Mishnah): We may put an egg in a mustard strainer.

(Yakov Korchah - Beraisa): This is permitted because it is done only for color.

Rishonim

Rambam (Hilchos Shabbos 9:14): One who makes dye is liable for Tzove'a (dying). E.g. he put vitriol in gallnut water, and made it all black, or Istis (woad, a plant that produces an indigo dye) into saffron water, and made it green.

Ra'avad: We learn Meleches Bishul from cooking ingredients [for the dyes] in the Mishkan. One should be liable [also] for dying the water! I say that one is liable only for dying the matter in which the Melachah is finished, but not for dying water, which one does not dye for its own sake.

Magid Mishneh: The Rambam explains that on 18a, we ask which Tana is Mechayev for putting water into dye, i.e. for Tzove'a. If something must be kneaded, the Melachah of Tzove'a is finished only after he mixes it. This requires investigation. The Rambam is correct. Indeed, he is liable also for dying. We learn [from making dye] that he is liable for cooking.

Rashi (140a DH l'Fi): One puts an egg in a mustard strainer only for color, for the yolk colors, but the white does not. Therefore, both of them are foods, and there is no Breirah of Pesoles (waste) from food.

Poskim

Shulchan Aruch (OC 320:19): One may put saffron in a Tavshil (cooked food) without concern for dying, for Tzove'a does not apply to food.

Beis Yosef (DH Kasuv): Shibolei ha'Leket suggests that perhaps we must be concerned for dying regarding saffron. The Yere'im holds that there is no problem. He says that one must be careful not to wipe blood or juice of berries or other fruits on garments, but one may color his bread, for Tzove'a does not apply to food.

Darchei Moshe (2): The Agur says that we are not concerned for this, since it is Derech Lichluch (dirtying), and not dying. R. Avraham Mintz forbids putting red wine into white on Shabbos due to dying. The Yere'im permits. A support for this is that we may put an egg into mustard, even though it colors.

Eshel Avraham (25): Tzove'a does not apply to food. One may put saffron in a Tavshil, or red wine into white wine to redden it. The Darchei Moshe says that this is Derech Lichluch, i.e. for a garment. He connotes that one may put red wine into white with intent to redden it. He learns from Siman 319, which permits putting an egg into mustard for color. However, the Magen Avraham (319:16) explains that the Rambam holds that eggs improve cloudy foods. If so, there is no proof from there. In any case, all could agree [that Tzove'a does not apply to food]. However, coloring whiskey or mead (a drink made from fermented honey), so that people will buy it, could be different. We permit saffron for the sake of eating. One may eat however he wants. Also, it will not last a long time. Dying for selling is like Shechitah. See 75b. The Magid Mishneh says that the Halachah follows Shmuel, i.e. when the Shochet did not intend to dye. Perhaps one is liable if he dyed a liquid so that people will buy it. All the more so one may not put [dye] ingredients in a bowl of water in the window, in the sun. All could agree that one is Chayav for this, for this completes the Melachah of dying.

Magen Avraham (321:17): Some are Mechayev for salting food to last a long time (a Toladah of tanning), because his act is not for the sake of eating [now].

Chacham Tzvi (92): The Taz (511:8) forbids putting scented oil in water for Kohanim to wash from, for this is Molid (creates) a scent in the water. He forbids even from Erev Yom Tov, for this scents the Kohanim's hands. I permit. This is no more stringent than dying, which is an Av Melachah. The Mechaber (320:20) forbids touching a tablecloth or garment with hands dyed from berries, but he is not concerned for the hands getting dyed! One may put fragrances into water on Shabbos for washing, just like one may put spices into a Tavshil without concern for Molid Re'ach. Molid Re'ach, and even dying, do not apply to food and drink, like 320:20 and Rashi (140a). This is not only if he intends to eat or drink it, rather, even for washing. This is not only according to the Ra'avad, who exempts for dying water. Even the Rambam is Mechayev only for dying something not proper for people to eat or drink. This is why the Rambam taught about Istis into saffron water, but not liability for saffron into water alone, for it is edible. Why does the Rambam rule unlike Rav regarding Shechitah? Perhaps Rav is Mechayev only because one may not eat it (the blood). A proof is that one may mix red wine with water on Shabbos, even though the water becomes red.

Question (Eshel Avraham): Perhaps the Rambam mentioned Istis into saffron water to teach that one is liable even though 1) it is not the final Melachah of dying, and 2) it was already dyed, and he merely changes it a little! All the more so one is liable for saffron into water alone. The Ra'avad exempts because the Melachah of Tzove'a was not finished. If it were finished, he would be liable, even for water! Tzove'a does not apply to food, for it does not last, but here is forbidden. This requires investigation. The Rambam (Hilchos Yom Tov 4:6) permits smoking Peros to eat them. This implies that one may not smoke food to smell it [and all the more so Tzove'a applies to food].

Note: Why does he infer that it is forbidden due to Molid Re'ach? The Rambam there discusses burning and extinguishing!

Eshel Avraham: The Shitah Mekubetzes (23a DH v'Rava) says that Tzove'a does not apply food and drink.

Hagahos Shulchan Aruch ha'Shalem (63): The Shitah Mekubetzes there discusses only Molid Re'ach!

Mishnah Berurah (56): The Pri Megadim permits putting red wine into white, even with intent to color. Nishmas Adam says to refrain from this. In any case one may not color whiskey or mead for sale. In any case it is Uvda d'Chol (a weekday action).

Bi'ur Halachah (DH Liten): Nishmas Adam questioned this from 75b, which shows that Tzove'a applies to food. However, Or Zaru'a explains that he wants to dye the hide [which is not edible]. If so, there is no difficulty.

Kaf ha'Chayim (113): Chayei Adam said that perhaps we permit only saffron, which is added for taste. If it is normal [to add something for color], perhaps he is Chayav Chatas! The Ben Ish Chai forbids regarding liquids, and permits regarding food.

Kaf ha'Chayim (115): One may soak raisins and peaches in water. We forbid only dye and ingredients that make dye.

Kaf ha'Chayim (116): One may not intend to color food, and one may not color liquids even without intent, for this is like making dye, for which the Rambam is Mechayev. One may put water into beer, even though it turns white, for one cannot do so from before Shabbos, lest it spoil, and some cannot drink beer without diluting it.

Kaf ha'Chayim (117): One may not mix red beer into white. One may mix white beer into red if he does not intend to color.

Shulchan Aruch (20): Some say that one who eats berries of other colored fruits must be careful not to touch his clothes or the tablecloth with colored hands, due to Tzove'a.

Magen Avraham (24): The Radvaz (131) calls this an excessive stringency, since it is Derech Lichluch. Some forbid laundering Derech Lichluch (302:10), and all the more so Tzove'a, for dying is always like this! One should not be lenient.

Magen Avraham (25): We are not concerned for coloring his hands and face, only for something normally dyed. This is unlike 303:25, for it is normal for women to color their faces.

Gra: This is like the latter opinion in Sa'if 18 [that forbids a Pesik Reishei d'Lo Nicha Lei].

Mishnah Berurah (57): Even though it is a Pesik Reishei d'Lo Nicha Lei, and it is Mekalkel, l'Chatchilah it is forbidden.

Mishnah Berurah (59): All the more so it is forbidden if the garment is red, for [the juice] improves it. Some are lenient about all this, for it is Derech Lichluch. One may rely on them when he cannot be careful about this.

Kaf ha'Chayim (120): If one is bleeding, he should not put a garment on it, due to Tzove'a. In pressed circumstances one may be lenient.

Kaf ha'Chayim (125): If one wrote on his hand and forgot [to remove it] before Shabbos, he may wash to eat, but he must pour a Revi'is at once [so he need not pour a second time] and dry them in the sun or leave them in the wind until they dry.

Shulchan Aruch (ibid.): There is no problem if he colors the bread through fruit juice, for Tzove'a does not apply to food.

Sha'ar ha'Tziyun (318:64,65): One may pour tea essence into water in a Kli Sheni, for we are not concerned for Tzove'a. If the essence is still warm, it is better to pour the [hot] water into the essence, to fulfill the opinion that is concerned for Tzove'a. See Ya'aros Devash (2, Drush 8).

Kaf ha'Chayim (318:65): The custom in Yerushalayim is to cook the leaves before Shabbos and leave liquid with them, and pour into the liquid on Shabbos, to avoid Tzove'a.