Woah...it's one of those questions. The "Computer simulation" argument of History if you will, and one which actually does not hold together upon some scrutiny. Now mind you I will not draw heavily on works of historical philosophy or historiography as a whole here, but for further reading on the importance of sources I wholeheartedly recommend picking up that titan of a work by the late Edward Hallet Carr, What Is History? (1961, ISBN 9780140227505). Let's begin then by dissecting the question and seeing if we can come to some result(s).

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How do we know what happened in the past?

In a slightly cynical view of History: we can never really claim to "know" what happened in the past. The past has existed and no longer does, and barring the creation of time machines in the distant future, a historian can never really experience the centuries, decades, years, or even weeks in history which they may be writing about. Now to temper that argument, we do need to acknowledge that memoirs, autobiographies, and historians writing about their experience of a historical event are certainly viable substitutes for a "time travel experience" of the past. Yet even then, what we know is based on what documented or physical information (especially in the case of archaeological evidence) of the past we can access. Archives, museums, and various collections have all contributed their fair share of responsibility to keeping the past "alive" (if such a term can be applied) for us to read and write about. For example, in my line of expertise I often find myself indebted to the fact that many pieces of inter-governmental correspondence at the outbreak of the First World War and prior to that remain, in some form or another, accessible to myself at the click of a button or the rummaging of a book.

With that in mind however, historians also have to realise that there will inevitably be "blank bits" in the narratives. Some due to lack of access to sources; such as western orthodox historians of the Cold War who could not (for obvious geopolitical reasons) access the confidential Soviet archives until post-1990. Others due to the fact that the sources simply do not exist; such as my annoyance at the lack of source-work confirming or denying official Serbian endorsement/knowledge of the plot to assassinate Archduke Franz Ferdinand (still, I try). In the case of the former, historians will usually go back and rewrite narratives based on newly available sources (hence the emergence of the post-revisionist school of Cold War historiography), and in the case of the latter it is up to the historian to "fill in the blanks" as best they can, or divert focus to a more important area of investigation.

To paraphrase a bit of Edward Hallet Carr, our sources can also be pre-decided for us. Some memoirs and personal accounts will likely be edited to portray the subject person in the best possible light, and omit (or at least attempt to explain) their shortcomings which portray them negatively. At the other end of the historical writing process, the historian themself is responsible for the selection of which sources to include and which to exclude in their writings. E.H Carr goes even further and argues that before the historian comes along, the past can also decide which facts are of note and which are minor footnotes. Historians of Ancient Rome for example, have many times over investigated the significance of Julius Caesars' crossing of the Rubicon, but gloss over the fact that hundreds of other people crossed the Rubicon before and after him (an example Carr brings up as well). In short, we know what happened in the past as a result of the sources which exist, floating around and waiting to be discovered, prepared, and served in all manner of historical narratives.

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How can we verify that it was true and not propaganda from the governing state?

That also depends on the nature of the source. Whilst secondary writings often have some form of agenda and/or bias imbued in them, primary sources written at the time of the event by a person who experienced it (in one way or another) can be a lot more revealing and lacking in such biases. I for example, comb through a fair bit of treaties, correspondence, and quotations from figures in late 19th century Europe, which represents the policies, fears, and desires of that age. Archives often hold stores upon stores of unedited writings from decades long gone, possibly including items written before the line between historical academia and state propaganda blurred and crossed over at times. It is up to the historian to sort out the biases, and note them for readers if they believe it is major importance (a good practice).

That at least, is my tuppence on this fairly interesting question on the practice of history. For some more discussions on related topics, I highly recommend searching AH's own archive of the Monday Methods features, especially on matters related to the sourcework of history and academic writing.