If you're completely new to American history, I'm assuming you want something that gives you an overall narrative of the 400 or so years starting with European settlement in North America (north of Mexico that is).

It's a bit tricky because there actually aren't that many single volume histories, at least nowadays, as it's something of a format that has somewhat fallen out of favor. There are microhistories (as mentioned), and there are some standard textbook histories for things like college courses, but these latter almost always come in two volumes (it's a very common practice to teach US history in two semesters, with the dividing line coming at the end of the Reconstruction Period in 1877). Samuel Tindall and David Shi's America: A Narrative History is the most-used example of these. High school courses like the Advanced Placement US History course tend to use a single volume textbook like David Kennedy and Lizabeth Cohen's The American Pageant. Eric Foner's Give Me Liberty!: An American History would be another such example used in AP US History and college classrooms.

There are also one-volume histories that have been produced to rectify deficiencies in the standard teaching of US history. Howard Zinn's People's History of the United States is probably the best-known example of this, as he criticizes US history from the left - issues with his methodology are discussed in this sub's FAQ. A right wing, triumphalist version is Larry Schweikart and Michael Allen's A Patriot's History of the United States. A volume that focuses on indigenous issues in US history is Roxanne Dunbar-Ortiz' An Indigenous People's History of the United States. Jill Lepore, a respected Harvard professor of US history, has recently written These Truths: A History of the United States that focuses heavily on US civics and political history.

Eric Foner's The Story of American Freedom is a one volume US history that might be worth checking out. I mentioned Foner above, and I am definitely a fan of his work - his main area of focus is the Civil War era and Reconstruction, and has written a number of in-depth works on those subjects (his massive Reconstruction: America's Unfinished Revolution, 1863-1877 and The Fiery Trial: Abraham Lincoln and American Slavery are excellent).

If you're looking for really short overviews of US history, something like Link Tullar's United States: A Brief Narrative History or Paul Boyer's American History: A Very Short Introduction (the latter is part of Oxford University Press Very Short Introductions series), might be a good place to start, but: they are really short - about 200 pages. You should definitely read them with an eye to checking out the suggested reading sections to get more information.

The most immediate recommendation might be for a narrative or a textbook, but I would argue that reading a microhistory of American history is much more interesting, and it might satisfy your needs as a foreign learner. Usually when American historians write micro histories, it is use either a specific case study or local study of a particularly small piece of history in order to elucidate and make sense out of a larger, more well-known event.

For example, Dr. Alan Taylor (a professor of early American history at the University of Virginia) wrote a book called William Cooper’s Town. This is considered a microhistory because Taylor researched local and parochial resources about a particular person and their local environments (Philadelphia and upstate New York). The reason why I mention this book, however, is because Taylor uses William Cooper (who was a real person) and his story as a way to explain broader topics and trends in American history. The American Revolution is understood, usually, as an event that totally turned the old American social order upside down. Before the Revolution, most wealthy and important men had achieved their status through their families or through political connections. Cooper became famous and well off through none of those means. Because of the Revolution’s effects, men like Cooper were able to rise through the social ranks without hereditary wealth or formal connections to politicians or gentry. He was a “self-man.” That is just one of Taylor’s threads throughout the book, but that is a good example of what microhistory does.

If you pick up a microhistory, you will learn about localized events, but the idea of a microhistory is to see how local events or people either influenced or were influenced by broader American trends, events, or wars. Naturally, you could always pick up a college textbook and read through that, but I think a better option would be a microhistory because you might find the characters interesting while also being able to grasp American history in a way where you aren’t overwhelmed or confused due to a lack of knowledge.

My two favorites are William Cooper’s Town and a book by Paul Johnson called “Sam Patch.” Johnson’s work is about a waterfalls jumper who lived in the 1820s. He was a real man who, through skill, was able to survive 100 foot jumps, without any safety equipment, into waterfalls. He even jumped into Niagara Falls! He was an interesting character, but out of Patch’s life and travels, Johnson is able to make larger points about social order, the industrial revolution, American conceptions of technology, aesthetics, and beauty, as well as temperance and 19th century reform movements.

Good luck and happy reading!