Here is a list of how the 8 Immortals did it:
He Xiangu "When she was about 14 or 15, a divine personage appeared to her in a dream and instructed her to eat powdered mica so that her body might become etherealised and immune from death. She did as instructed and also vowed to remain a virgin. She also gradually decreased her food intake. One day she ascended to Heaven in broad daylight and became an immortal."
Cao Guojiu "Cao's younger brother abused his relationship with the imperial family by bullying others and engaging in corrupt practices. Cao tried to persuade his brother to change his ways but he did not listen. In the meantime, he also used his family fortune to help the poor and tried to make up for his brother's misdeeds. One day, the brother was accused by other officials in the imperial court of corruption and abuse of power. Cao felt so ashamed and disappointed by his brother's misconduct that he gave up his official career and went to the countryside to lead a reclusive life. During this time, he met the immortals Zhongli Quan and Lü Dongbin, who taught him Taoist magical arts. After many years of practice and cultivation, Cao himself also became an immortal."
Li Tieguai "Li studied with Laozi, the founder of Taoism. He is said to have renounced material comforts and led a life of self-discipline as an act of religious devotion for 40 years, often going without food or sleep. Li lived in a cave in the early stage of his Taoist training. Laozi tempted him with a beautiful woman he had made of wood. After refusing to acknowledge the presence of this woman and therefore defeating his temptation, Laozi told him of his trick and rewarded him with a small white tablet. After consuming this tablet, Li was never hungry nor ill. Laozi tempted Li again with money. Some robbers had buried money in Li's field without knowing he was watching. Laozi approached him in disguise and told him he should take any money that came to him. After Li refused, saying that he did not care if he remained poor his whole life, Laozi rewarded him with another pill. This pill bestowed upon Li the ability to fly at amazing speeds. On one occasion, his spirit travelled to Heaven to meet other immortals. He had told his apprentice, Li Qing, to wait for seven days for his spirit to return. If he did not return by then, Li Qing was to burn the body because that meant that he had become an immortal; but after six and a half days Li Qing had to go home to see to his sick mother one last time before she died. Li Qing thus cremated Li Tieguai's body. He passed by a dying beggar on his way to his mother's but did not have time to bury him. Upon returning, Li Tieguai's spirit found that his body had been cremated and had to enter the only body available at the time was the corpse of the and ugly, homeless beggar with a lame leg who had just died of starvation. Laozi appeared and gave him a medicine gourd that could cure any illness and never emptied. Li then brought his apprentice's mother back to life using the liquid from his gourd. Li Qing was then dismissed as his apprentice, after being given a small pill and being told that he would work hard enough to become an immortal himself. This turned out to be true.
Lan Caihe "Lan was said to have been in a drunken stupor when they left the human world by riding on a celestial swan or crane into Heaven. One legend says that they became an Immortal with the help of Sun Wukong, who transferred 500 years of magical powers to them." [Note: "they" is used as the gender neutral singular pronoun, and Lan is androgynous.]
Lü Dongbin "A story has it that when in Chang An, Lü was tested by Zhongli Quan ten times before Quan took him in as a disciple and Lü subsequently became immortal." Lü's Ten Trialsshow Lü him to be an exceptional person, both in virtue, humanity, courage and constitution, certainly worthy of immortality.
Han Xiangzi There doesn't seem to be a specific story as to how Han achieved immortality, aside from being a student of the magical arts under Lü Dongbin.
Zhang Guolao "A strong believer in the magic of necromancy, he was also known to be a master of qigong and could go without food for days, surviving on only a few sips of wine." The implication is that he he studied and practiced to the point where he achieved immortality.
Zhongli Quan "There are two stories that depict how he became one of the immortals. In the first, it was in his continuous use of the immortal powers and his magical fan that eventually caused his descent into the shimmering cloud of the immortals. In the second, he was meditating near a wall of his hermitage when all of a sudden it collapsed. Behind the wall was a jade vessel that took him as an immortal to the shimmering cloud."
This is pretty good summation of the overall concepts:
"The Eight Immortals are examples of how all can obtain immortality. Most of the immortals were common folk who attracted the attention of the gods through suffering unjust treatment, without complaint, and gave more to others than themselves. They were admitted to eternal life as a reward for their acts on earth and bearing gifts to the Old Man of the South Pole, the god of longevity. 'The path to immortality includes achieving physical and spiritual harmony through meditation, diet, exercise, breath control, and the use of herbs. To achieve this state, one also had to eliminate all disease and evil from the body and spirit'."
[You can find the text and citations for this summary here]
I basically lifted this from Wikipedia. Many, but not all, of the quotes have citations there. However, all of the stories are consistent with what I've read, seen, and had recounted to me.