Historians ask many things. Of course, they study specific time periods and specific topics and they ask many questions about those topics. There are almost infinite numbers of questions that could be asked because there are so many different topics that could be studied. This being the case, we have to look at more generic questions that historians try to ask about various times and topics.
Historians sometimes ask how people experienced things in their particular time in history. For example, historians can ask how women experienced life in the United States in the 1950s. They could ask how it felt to be a slave. In asking things like this, they try to understand how people actually experienced the events that we now call history.
Historians sometimes ask what lessons we can learn from history. For example, many historians have looked at the Vietnam War and asked what we can or should learn from it. They try to determine what that war tells us about whether/when we should intervene in conflicts in distant countries. This allows them to say things that have practical uses in our own time.
Perhaps the most important thing that historians ask is “why.” Historians want to know why things happened as they did. For example, a historian might ask why Japan invaded China in WWII or why Japanese troops were as brutal as they were in that war. A historian might ask why the United States chose to drop atomic bombs on Japan at the end of the war. This is the most important thing that historians can ask because the answers to such questions can help us understand what lessons history can teach us.
Historians ask all of these things and more.