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Where can you discover water? Where does ground water occur? Or where do streams flow inside the earth? By what signs on the surface do you make out the presence of water underground? How are perfumes manufactured? What are the right measurements for a house? These questions are discussed in the samhita-skandha of Jyotisa. Also omens and signs.
"Sakuna" is one thing, "nimitta" quite another. "Sakuna" literally means a bird: only signs connected with birds come under the category of "Sakuna". All things in this world are interrelated: all happenings are linked to one another. If we know the precise scale and manner in which events are woven together, we would be able to know everything. Everything in this world occurs according to the will of the One Being and according to a precise system. So with reference to one we can know all others. Palmistry, "arudam" (a method of divination), astrology, all are interrelated.
What does a bird flying from right to left indicate? What is foretold by the chirping of such and such a bird? Question like these belong to the sakuna-sastra. "Nimitta" means omen. "Nimittani ca pasyami viparitani Kesava" says Arjuna to Krsna before the start of the battle of Kuruksetra. He uses the right word "nimitta" while we use the word "sakuna" carelessly. When a cat crosses our path it is an omen; when an eagle flies above us it is a sakuna.
To go back to Arjuna. The Lord tells Arjuna: "Nimittamatram bhava Savyasacin". This is in answer to Arjuna telling Krsna, lamenting, that it is sinful to kill one's enemies [or one's kin]. Says krsna: "I have already resolved to slay them in this battle. So they are already as good as dead. It is I who will kill them. You are a mere tool" (Nimittamatram bhava).
A nimitta does not produce any result on its own. It points to the result that has already been ordained by some other factor--or, in other words, it merely indicates the fruits of our past karma.
For a general background, please see here