In the Undying Lands at about TA 1000, Manwe summoned a council of the Valar to send three messengers to Middle-earth. Two Maiar came, Curumo (Curunir or Saruman) sent by Aule, and Alatar, sent by Orome. Manwë asked where Olorin (Gandalf) was, and he came, after returning from a journey. Manwë asked Olórin (Gandalf) if he would go as the third messenger. Olórin said that he was too weak, and he was afraid of Sauron. Manwë said that that was all the more reason to go, and that he commanded Olórin to go as the third. Then Varda said "Not as the third." Yavanna begged Curumo to take Radagast, and Alatar took Pallando as a friend.
They were forbidden to dominate the peoples of Middle-earth or to match Sauron's power with power. When Saruman, the greatest of the Wizards, disobeyed this injunction, he was cast from the order and banished from the Undying Lands (Valinor).
Arrival and Second Age
Most were given different names from before they had come and they arrived in different colours of clothing from each other, and they were called Wizards. Many of these wizards came to the northwestern regions of Middle-Earth . The chiefs of those that came to Middle-earth were five in number. When the five Istari came to Middle-earth sent by the Valar they where known as the Order of Wizards. After they have arrived, the two Blue Wizards (Alatar and Pallando) went into the east and no one heard from them again. Radagast, the Brown wizard liked the nature, animals and other creatures, and so he lived in Mirkwood amongst the Sindarin Elves, befriending Beorn and his perople, and lived there for many years.
The other two wizards, Curunir and Olórin have gone to the other elves, Dwarves and Men. Curunir, now known as Saruman was wise and respected enough by all that he had become head of the Istari in TA 2463. He also befriended Treebeard and walked in his forests. He was given Orthanc by Gondor as a base as a reward for his services. Here he discovered an ancient Palantir, and from there Sauron began his corruption.
Soon, his pride made him get jealous of Gandalf who was given one of the 3 rings of the Elves. This caused him to slowly betray the original purpose of the Istari as he slowly made plans to acquire the One Ring.
During this period, 3 of the Istari are influential: Gandalf, Saruman and Radagast. Although the latter had the smallest part to play. We first meet Gandalf, during the Hobbit when he assembles his dwarven clan for a "Treasure Hunt". Along the way the group travel to Mirkwood where they meet Radagast who is enjoying himself amongst the flora and fauna. Thy have an amazing adventure which results in the great War of Five Armies. During this time, Saruman was sending many of his Uruk-Hai to scour the river where the ring was last seen, and start building his army.
He has also sent his envoy Grima Wormtongue to Rohan where Saruman takes control of King Theoden's mind and so exerts his control over Rohan.
During this time the blue wizards (Alatar and Pallando) are said to have instigated the Easterling and Haradarim religion and may have brought the into the War of The Ring.
The War of The Ring
The biggest Istari involvement here is in the first part. Following the discovery of the Ring, Gandalf goes to Saruman to report his findings. Along the way he encounters Radagast who tells him how Saruman has changed. Gandalf and Saruman have a disagreement regarding what to do with the Ring. Saruman has already been corrupted and believes that they should use the ring to overthrow Sauron. They have a short fight during which despite dealing some injuries to the head of the White council Gandalf loses. He is imprisoned upon the top of orthanc. Fortunately Gandalf summoned his friend Gwaihir, the Lord Of The Great Eagles of Manwe.
Gandalf returns to the fellowship and leads them through the Mines of Moria, where he encounters one of the Last Balrogs, Durin's Bane. Here he defeats his fellow maia however at the cost of his own life. He was returned to life however by Eru who decided his help was still needed. He was returned as Gandalf the White and was given all the power and authority Saruman should have had.
During this time Saruman sends his first wave of Uruk-hai to hunt down the ring and capture the halflings who carry it. These Uruks cause the splitting up of the Fellowship, with Frodo and Sam going to Mordor and Aragorn, Legolas and Gimli pursuing the captured Merry and Pippin, and the death of Boromir.
Saruman is overthrown from Rohan by Gandalf and The Three Hunters (Legolas, Aragorn and Gimli) who throw out Grima causing Theoden to regain control. In retaliation Saruman launches his entire army to Helm's Deep where they are ultimately annihalated. Orthanc is overcome by Ents, following The Last March Of The Ents led by Treebeard. Saruman is imprisoned alongside Grima.
In the film Grima kills Saruman atop Orthanc while they are both imprisoned. In the books and comics Grima and Saruman return to the Shire (albeit powerless) and under the name of Sharkey Saruman instigates a rebellion and seizes control until he is fought by Frodo, Sam, Merry and Pippin who have returned from overthrowing Sauron. He is then killed by Grima who slits out his throat (in the film he is stabbed in the back twice).
Following this only Gandalf is spoken of leaving Middle Earth for Valinor giving up his ring (Narya, ring of fire) taking with him Frodo and Bilbo.