The planet Saturn is a representation of Lord Sani. By the movement of Saturn, we understand the intentions of Sani. He is the natural ruler of karma, and to understand our karma, we must first understand Sani. Sani is one of the three children of Sun and Chaya Devi. From the Vedic texts, we learn a lot about Sani. Many times the power of his gaze has been mentioned in the classics. We learn that right after Sani was born, his gaze caused Sun's charioteer to fall and break his thigh,Sun's horses were blinded; and Sun himself was affected by his powerful gaze. They were healed only when Sani looked away.
Sani is usually considered a very malefic planet. The nine planets bestow on us the result of our karma - which are the lessons we need to learn. And most of the times, the toughest lessons are taught by Sani. Different planets teach us different kind of lessons, and most of the time the teacher Sani teaches us very painful lessons. Hence Sani is considered the most malefic planet, and the most problematic, painful yogas involve Sani most of the times. 
When Sani affects us, he slows everything down, causes obstructions and delays.Sani also rules separation, he hurts by taking things away. When we face a painful separation from our parents, spouse, friends or anyone we care for, Sani is always a possibility for that. Ketu also causes separation as he rules non-attachment, but separations and delays are among the main manifestations of the malefic effects of Sani. His association with Venus causes separation from spouse at most times. 
Favourable effects of Sani on one's nature include in-depth knowledge, sensibility, wisdom, justice, broadness of mind, honesty, patience, ability to work hard etc. In life, he may give wealth, fortune, long life etc. when auspicious and well placed.On the other hand, when badly afflicting a person's nature, Sani can make one sadistic, greedy, lazy, dishonest, fearful, irresponsible and prone to addiction. Sani causes obstruction, delay, grief, poverty, short life etc. He makes a person totally lonely, helpless and can make one suffer from enmity, theft, lawsuits etc. Sani can also give imprisonment since he rules obstruction, loneliness and grief.When causing diseases, Sani generally gives chronic diseases as the person suffers for a long time.When badly effecting one's profession, Sani makes one work very hard but does not give the proper reward he deserves. That is why social servants and people who earn their living by physical labour are ruled by Sani. 
Among the planets in Vedic Astrology, Saturn is the last one counted from Sun's position. That is why Sani Dev rules 'The last' or 'The end' of anything. He is the 'Last Answer' in anything. In our world, death is the end of everything, and that is why, Sani rules death and longevity issues. He is the natural significator of 8th house in astrology which affedts sorrow, shock, pain, depression and also the occult. That is why Sani also deals with Magic, Tantra, Jyotish etc.
Sani was lamed by another son of the Sun, named Yama (God of death) when he hit Sani in his leg. So Sani is always very slow in his movement. One name of Sani, as I already mentioned, is 'Shanaischaram' which means the slow mover. He takes around 2.5 years to pass through a sign, thus he takes around 30 years to complete the travel over the whole zodiac. So he rules slowness and delays; And he teaches us how to tolerate slowness and delays, by patience. He is generally pleased with people having patience.
The great phase (Maha Dasha) of Sani lasts for 19 years. Even than the Maha Dasha, Sani gets the strong hold of a person by his transit over the 12th, 1st and 2nd signs from his or her natal Moon. This is called 'Sade Sati' since it lasts for about 7.5 years.
One of the ways to appease Lord Sani include offering of black clothes, mustard oil, black daal, sesame etc. to the poor and helping and serving the old and needy people since Sani signifies all these.