My conception is that for a long time immigrating to the US simply meant showing up. And I guess not being obviously dying of cholera.
I know that even before Ellis Island there were immigration processing stations but where there ever any checks on a person's background? Were immigrants required to enter at these stations or could they just get on any boat bound for the US?
Immigration to America, and eventually the independent United States has been constantly changing throughout the centuries. It also varied greatly from place to place.
In the early days of English colonization of America, meaning around 1620-1640, otherwise known as the Great Migration, the majority of the people moving to America would do so by going with their religious groups. These groups would get funding to go to America through a company, such as the Massachusetts Bay Company. With this funding, they would get passage to the New World. However, the price of this was to be an indentured servant, normally for the period of 4-7 years. It is estimated that around 80% of people immigrating to America in this period came as indentured servants.
When arriving at the colony, the people who were arriving as indentured servants would be put to work quickly. Also, their indentured servant contract often could be extended for breaking any contract rules. Examples of this included running away, or in some cases, becoming pregnant.
There were no real restrictions on immigration to America until after the United States won their independence. For example, the first law about citizenship passed in 1790, allowing unindentured, white males citizenship after 2 years of residency.
The first law about "checkpoints", to know who and what was coming into the country, was passed in 1819 called The Steerage Act. This law required ship captains to submit a manifest giving information about the immigrants.
In 1891, the Bureau of Immigration was founded, and began officially processing immigrants. They founded Ellis Island, as well as many other processing locations. This was the point the United States officially began processing everyone who immigrated there.