There was not a single, unified kind of relationship between the United States an all Native Americans in the 1830s, but that decade's most noteworthy event in U.S.-Native relations was the forced eviction (or "relocation") or a number of Native communities (most famously the Cherokee) to land much farther west. The Cherokee are native to what is now North Carolina, South Carolina, and Georgia, but under Andrew Jackson the U.S. passed the Indian Removal Act, which violently forced the Cherokee to leave their homeland and move to a reservation in what is now Oklahoma.
In the 1830s the relationship between the U.S. and Natives was also importantly defined by a Supreme Court Case called Cherokee Nation v. Georgia, in which the Court ruled that only the federal government, and not the states, could make treaties and agreements with Native tribes. This means that the 1830s were characterized by the federalization of Indian relations (in other words, the job of making arrangements with the tribes was transferred to the federal government and away from the states).
