Before ASL?

American Sign Language, as we know it today, grew out of the first permanent school for deaf children in the U.S., which was founded in 1817 in Hartford, CT. It grew out of a combination of multiple sign languages and home signs brought by those students who did not previously use formal sign language at home. So to ask, strictly speaking, about how deaf people were treated before ASL means to ask how they were treated before 1817 - and the answer to that is "pretty well actually," because there were some alternatives.

Martha's Vineyard

A sign language used in the U.S. that predates ASL is Martha's Vineyard Sign Language. Extinct since the 1950s, it was a full-fledged language that originated in Martha's Vineyard in the 1700s, where intermarrying caused an exceptionally high proportion of the population to be deaf. MVSL had its origins in sign languages or systems used in Kent, England, as many of the early migrants to Martha's Vineyard were from that region. So people communicated just fine without ASL on Martha's Vineyard, because they used MVSL. Deaf people were treated as any other member of the community. MVSL was one of the languages that contributed to the formation of ASL, as when the school opened at Hartford, students from Martha's Vineyard attended and brought their language with them.

Unfortunately, MVSL died out before ASL was recognized as a language. There was no linguistic study of either one during the time they co-existed, so it is not known what signs the two may have had in common.

For further reading about Martha's Vineyard, try Nora Ellen Groce's book Everyone Here Spoke Sign Language.

Deaf People in Rural/Pre-Industrial US

Even after the founding of the American School for the Deaf in 1817, there were still many states with more rural populations, whose deaf citizens did not participate in the burgeoning deaf community in more populated areas. There is substantial evidence of their participation in society, though, with some being taught to speak and others "making themselves understood" by signs or gestures. This is most likely home signs, which also contributed to the formation of ASL, but which is not considered a formal language. Nonetheless, home signs have been effective for centuries at allowing a deaf person to participate in society. There are records of deaf marriages, land ownership, tutoring/schooling, and other activities from the late 1600s to the early 1800s, indicating that formal schooling was not necessary for someone to communicate and be a participating member of society.

For more on this, read Harry Lang's chapter "Genesis of a Community: The American Deaf Experience in the Seventeenth and Eighteenth Centuries" in The Deaf History Reader, edited by John Vickrey Van Cleve.

Another good reference is The Deaf Community in America: History in the Making by Ron and Melvia Nomeland.

More?

I can go a bit earlier too, if you're interested. Touch on communication and societal perception of deaf people in 16th century Europe, etc. I figure that's enough for now, though, and might mostly answer your question. Let me know if you'd like more.