Saturn is the slowest planet in the solar system that is relevant to Vedic/Indian Astrology. It takes 29.5 years to complete one revolution around the Sun. Considering 12 rashis, it would be in one rashi for 29.5/12 ~ 2.5 years. In Gochara, Saturn's transits are given a lot of importance because it stays in a rashi for the longest time. In general, Saturn is associated with qualities of being cold and heavy like the metal iron. It destroys attributes of the house it is associated with by its association or drishti. Being the slowest planet, it also causes delays and is retarding in nature. Sadhe sati is referred to the seven and a half year period when Saturn transits over natal moon and adjoining houses. Translating this to from Astrology to English would take some effort :-). Consider a person who has his/her Janma Rashi as Aries, i.e. in the chart prepared during his/her time of birth, Moon is situated in Aries. Now, when Saturn moves through zodiac and comes to the sign of Aries, it is said to be transiting over Aries. In case of this person, adjoining houses would mean Pisces (one before) and Taurus (one after Aries). Thus, Saturn's transit over the three houses comprises of a total duration of 3*2.5=7.5 years. This 7.5 year duration is called in Hindi as Sadhe Sati. This cycle repeats every 30 years and thus a person with normal life span would see at least 2-3 sadhe satis in his/her life.
In both Western and Indian astrology, Saturn has been accorded the status of the most dreaded planet. In Indian mythology, it is the estranged son of Surya (Sun). Saturn is considered the opposite of Sun in many ways. Sun represents light, Saturn represents darkness. Sun is representative of kings and leadership in the society. On the other hand, Saturn represents poverty and the stark reality of the masses. Sunlight is the basis of all life on earth. Saturn is associated with obstruction and hindrance and ultimately, death. No wonder Saturn and Sun are exalted and debilited rashis exactly opposite each other. In Aries and Libra respectively. Saturn is associated with iron, the stuff bullets, swords and spears are made of. Mars may be the lord of war, but Saturn is what causes and executes it.
Saturn's transits over the three houses tend to bring a lot of depression to the person. He/she would face losses, delay or denials in new projects and health problems. It can also affect peace of mind and make a person emotionally unstable. The first round of sadhe sati affects the individual personally. There is a loss of health and wealth - miseries. The second round affects the person's parents and there would be some loss in the family. The third round is said to affect the children and bring the end of the person.
The above paragraph is what the real effect of Sadhe Sati is made out to be in a lot of books and astrology sites. However, sadhe sati does not affect each and every person in the same way. The effect also depends on which Sadhe Sati is in progress. The rest of this article is an attempt to describe these effects.
To understand how sadhe sati would operate, the first and foremost thing is to find out if Saturn is a functional benefic in the chart. The ill effects would be mitigated in this scenario. Saturn would be a benefic if:
It is a natural friend if the Rashi lord and Lagna lord,
It is a Rajyoga karaka planet,
It is lord of lagna, 5th house or 9th house in the chart.
Right away, we can see that for people with Taurus, Libra, Capricorn and Aquarius lagna/rashi, sadhe sati would not be bad. In fact, such transit of Saturn over lagna would be good for the person. For a transit over the rashi, there would be some emotional problems, as Moon is not happy when it is around Saturn (or Rahu as well for that matter).
The effects would not be good for rashis - Aries, Cancer, Leo and Scorpio as these belong to natural enemies of Saturn. Mercury and Venus are its friends and Jupiter is a neutral - hence there would be not much of a problem for the rest of the rashis. The exact effect would also depend on the position of Moon in a chart. If the Moon is in 1st house or in Aries, the transit would cause trouble in upper part of body. While transiting through 5th house, the problem could happen to the person's children, 7th house transit would be bad for the spouse etc.
Bad effects of Saturn and sadhe sati are mitigated by praying to Lord Hanuman who has special control over Saturn. Saturn is said to be forever in debt of Hanuman (see wikipedia article on Hanuman for some details) who had rescued him from the clutches of Ravana. Hence Saturn promised Hanuman that those who prayed to him (Hanuman) would be rescued from painful affects of Saturn.
In the first part of this article, I mentioned that Saturn represents death and the stark reality of the masses. This quality of Saturn can be put to a very positive use - it takes a person away from the moh-maya of this world. It teaches us a lesson like the other teacher - Jupiter, just the way of teaching is different.