Gemara

65b (Beraisa - R. Shimon): Me'onen is one who puts semen of seven men on the eye;

Chachamim say, it is a sleight of hand magician;

R. Akiva says, it is one who 'calculates' good or bad times, e.g. today is good to embark, tomorrow is good to buy, wheat is good in Erev Shemitah, if one uproots legumes without harvesting them they will not rot or grow wormy.

(Beraisa): Menachesh is superstition, looking for or acting according to omens like the following: His bread fell from his mouth, his staff fell from his hand, his son called to him from behind him, a deer crossed his path, a snake was on his right, a fox was on his left, do not collect the tax from me first, I do not want to pay my debt now, it is the start of the day or week or month.

(Beraisa): "Lo Senacheshu v'Lo Se'onenu" refers to people who look for or act according to omens of weasels, birds and fish.

95a: Once, on Erev Shabbos, Avishai ben Tzeruyah saw drops of blood (some say, he saw a dove shaking itself in front of him - Yisrael is compared to a dove, "Kanfei Yonah Nechpah ba'Kesef.") He deduced that David was in trouble - he looked in David's house, and did not find him.

He asked Rabanan 'we may not ride on a king's horse, nor sit on his throne, or use his scepter. Does this apply even at a time of danger?' They said that it does not. He took David's mule to ride on.

Shabbos 67b: Darchei ha'Emori applies to saying 'slaughter this rooster because it crowed Aravis (like a raven; alternatively - later than the others)', or 'slaughter this hen because it crowed like a rooster.'

Gitin 45a: Rav Ilish was taken captive. He found a man who understood bird language. A raven was chirping at Rav Ilish. The man said that it was telling Ilish to flee. Rav Ilish said that one cannot rely on ravens, for they lie. A dove chirped at Rav Ilish. The man said that it was telling Ilish to flee. He said 'Keneses Yisrael is compared to a dove. Surely, a miracle will be done for me! Rav Ilish fled with the man. Rav Ilish escaped; the man was caught and killed.

Rishonim

Rambam (Hilchos Avodah Zarah 11:4): One may not be Menachesh like Nochrim. E.g. he says 'since my bread fell from his mouth, or my staff fell from his hand, I will not go to the place Ploni', or 'if I go, I will not succeed.' 'Since a fox passed on my right, I will not leave my house, for if I do, a swindler will harm me.' The same applies to people who hear birds chirping and say that certain things will or will not happen, or it is good or bad to do certain things. He says 'do not collect the tax from me first, I do not want to pay my debt now, it is the start of the day or week or month.' The same applies to one who says 'slaughter this rooster that called at night, or this hen that called like a rooster.'

Ramach: The Gemara says that one may slaughter it, and it is not Darchei ha'Emori!

Kesef Mishneh: The Ramach had a mistaken text. Our text, which is Rashi's and the Rambam's, forbids.

Rashba (Teshuvah 283 attributed to the Ramban, in Beis Yosef ibid.): The Rambam says that all this is folly. The Sugya shows otherwise, even regarding Nichush, like the case of Rav Ilish. These matters require investigation. One should not be too exacting with people about them.

Nimukei Yosef (16b DH Tanu): He does not want them to collect the tax from him first, or at the start of the day or week or month, for it is a bad Siman (omen). The matters mentioned here are folly. There is no reasoning why they show that he will succeed or fail. If one recognizes the chirping of birds, this is not Nichush. Rav Ilish relied on this! Avishai understand from a dove that David was in trouble. This was not Nichush, for he did not totally rely on it. He merely considered it a Siman.

Note: he relied on it to ride on David's mule!

Beis Yosef (YD 179 DH v'Al): The (Rashba Teshuvah 283 attributed to the) Ramban says that the custom is to marry only when the moon is being filled is not Nichush. Just like we anoint kings near a river so that their reign will endure (Horayos 12a), we marry only when the moon is waxing, and not when it is waning, for a good Siman, just like we draw wine in tubes in front of Chasanim, and Darchei ha'Emori does not apply. Semak says that the custom to begin Masechtos on Rosh Chodesh is to wait for Bochurim coming from outside the city, and for a good Siman. Even though there is no Nichush, there is Siman.

Poskim

Rema (YD 179:1): The custom is to begin learning on Rosh Chodesh. Even though there is no (Heter to follow) Nichush, there is Siman. If one knows that something opposes Mazal, he should not do it and rely on a miracle. However, one should not investigate this due to "Tamim Tihyeh..."

Beis Yosef (DH Kosav ha'Rambam): The Rambam (Perush ha'Mishnayos Avodah Zarah 4:7) says that Me'onen is one who calculates good and bad times for journeys. He says that it is all folly, and therefore the Torah forbids it.

Darchei Moshe (1): Even the Rambam says so only if there is no medical support. We find that the Gemara gave good and bad times for cures and bloodletting (Shabbos 129b). Darchei ha'Emori does not apply to anything with a medical basis (Shabbos 67a). The Rashba (413) permits Segulos using bones or words as long as they help, even if there is no natural explanation. If one used witchcraft against Levi, Levi may use witchcraft to save himself.

Shulchan Aruch (2): The custom is not to begin (a task) on Monday or Wednesday. We marry women only when the moon is (past being) full (the latter half of the month).

Beis Yosef (DH v'Al): The (Rashba, Teshuvah 283 attributed to the) Ramban says that things done for a good Siman are not Nichush. We anoint kings by a spring so that their reign will continue, and we draw wine in front of Chasanim.

Gra (5): Many other things are done for a good Siman, e.g. the special foods we eat on Rosh Hashanah, marrying a virgin on Wednesday due to the Berachah to fish, and a widow on Thursday due to the Berachah to people...

Shulchan Aruch (3): One may not say 'my bread fell from his mouth, or my staff fell from his hand, my son calls me from in back, a snake passed to my right, or a fox to my left', and due to this he does not travel or begin Melachah. The same applies to Nichush through weasels, birds, or stars, or saying 'do not collect from me. It is morning, Motza'ei Shabbos or Motza'ei Rosh Chodesh', or 'slaughter this rooster that called like a raven, or this hen that called like a rooster.'

Rema: Some say that if he does not say why he commands to slaughter it, he just says 'slaughter it', it is permitted. This is the custom.

Beis Yosef (DH u'Mah she'Chosav v'Chen): Some (Maharil 111) say that the custom is to slaughter a hen that called like a rooster because R. Yehudah ha'Chasid commanded. Once, Mahara said that it is Darchei ha'Emori only when he says that he commands to slaughter it because it called like a rooster. If he says Stam to slaughter it, we are not concerned. Perhaps people rely on the Ramach's text, which permits.

Objection (Gra 8): This is like trying to fool Hash-m! Rashi (DH Yesh) had the Ramach's text, but he rejected it. Also the Rashba (413) says that this was the text.

Shach (3): Nowadays people explicitly say to slaughter it because it called like a rooster. They rely on the Ramach's text.

Shiyurei Berachah (Birkei Yosef, 6): It is brought in the name of Maharikash that anyone may open a Torah to see the verse that will come up, for it is our life. We find that Yoshiyahu found a Sefer Torah rolled to a particular verse. Yalkut Shimoni (Mishlei 960, DH ha'Lo) permits taking counsel from the Torah, i.e. in this way. Ba'al Shevet Musar says that when his Rebbeyim had a Safek what to do, they would open a Chumash or Nach, and act according to the first verse on the Daf. This is not called (improper) use of Torah. The Sifri forbids lotteries, but this is permitted.

Ha'Ga'on (3 p.1115,1122-23):. Many Gedolim used Goral ha'Gra (to find a random verse) to decide whether or where to relocate during and after the world wars. The Chafetz Chayim said that one must have great merits for Goral ha'Gra to work. If not, it can cause one to err. One should not 'burden' Hash-m by casting the Goral unless it is utterly essential.

Note: Perhaps the 'burden' to Hash-m is to expect Him to arrange that the Chumash was written in such a way that the proper verse appears in the right place on the Daf!