Born in Templeton, Massachusetts, Andrews went to Louisiana at age 18 and studied and practiced law there; appalled by slavery, he became an abolitionist. He was the first counsel of Mrs. Myra Clark Gaines in her celebrated suits. Having moved to Texas in 1839, Andrews and his family were almost killed because of his abolitionist lectures and had to flee in 1843. Andrews travelled to England where he was unsuccessful at raising funds for the abolitionist movement back in America.
While in England, Andrews became interested in Pitman's new shorthand writing system and upon his return to the U.S. he taught and wrote about the shorthand writing system, and devised a popular system of phonographic reporting. To further this he published a series of instruction books and edited two journals, the Anglo-Saxon and the Propagandist. He devised a "scientific" language, "Alwato," in which he was wont to converse and correspond with pupils. At the time of his death Andrews was compiling a dictionary of Alwato, which was published posthumously. A remarkable linguist, he also became interested in phonetics and the study of foreign languages, eventually learning 30 languages.
By the end of the 1840s he began to focus his energies on utopian communities. Fellow individualist anarchist Josiah Warren was responsible for Andrew's conversion to radical individualism, and in 1851 they established Modern Times in Brentwood, NY. In 1857 Andrews established Unity Home in New York City. By the 1860s he was propounding an ideal society called Pantarchy, and from this he moved on to a philosophy he called "universology", which stressed the unity of all knowledge and activities.
Andrews was one of the first to use the word "scientology". The word is defined as a neologism in his 1871 book The Primary Synopsis of Universology and Alwato: The New Scientific Universal Language. Andrews was also considered a leader in the religious movement of Spiritualism.
Like most of the nineteenth century individualist anarchists, and unlike the anarcho-communists, he supported the right of employment and wage labor. However, he believed that in the system within which he was living that individuals were not receiving a wage commensurate with the amount of labor they exerted. He said:
For Andrews, to be paid "justly" was to be paid according to the "Cost Principle," which held that individuals should be paid according to the amount of labor they exert rather than according to the benefit that another receives from that labor (the latter being called the "Value Principle"). To help make this simple, he, after Josiah Warren, advocated an economy that uses "labor notes". Labor notes are money marked in labor hours (adjusted for different types of labor based on their difficulty or repugnance). In this way, it is not how much the employer values the employee's labor that determine's the employee's pay but simply on how much the employee has labored. For similar reasons he did not believe people should be paid interest for loaning capital; in other words, he did not see the loaning of capital as requiring any labor or deprivation on the part of the loaner. He insisted that the benefit received from goods or labor is not a just measure of price.