Answer questions and tell stories, if you want the broadest answer. More specifically, try to answer questions that are relevant to understanding the past through research. The research may consist of going to archives that have files that are relevant (want to know about atomic history? Maybe go to the Department of Energy's archives in the National Archives), interviewing people (go interview former atomic scientists), using statistical data (how much funding was going to atomic research relative to other fields of science/technology, and how did that change over time relative to GDP and number of people involved?), or whatever other tools you can think of to answer you question. Then you write articles to communicate your arguments to other historians; write books that expand on those arguments; teach the subject matter at a broader level, but informed by your research, to undergraduates; and sometimes do outreach work like op-eds, podcasts, blog entries, public lectures, etc. Plus all the politics of academia.
So I'm a historian. My wife is a historian. Many of my friends are historians.
What we do:
I currently have a fellowship at an independent organization that supports history, and I can do pretty much whatever I want as long as it is "work" and I do things for the organization when they need me to. My day-to-day work includes reading, researching (either in archives or with databases), writing (I blog, I write articles, I am finishing a book), and, like all people, answering a lot of e-mail. (At the moment it includes applying for jobs, as well, because my fellowship is fixed term.) And I'm currently teaching a course at a local university, so that means I prepare two 90 minute lectures a week, prepare assignments and tests, and help grade said assignments and tests. And meet with students outside of class to help them on their papers, etc. And I give lots of talks and lectures, either at conferences or other universities (if they are local or will pay me to go visit them and talk).
My wife decided academia wasn't very fun and became a teacher of history at a high-end private school. She loves it. Let me tell you, you wish my wife was your history teacher. She knows the content (she has a Ph.D.), she knows how to teach, she makes it incredibly interesting and incredibly fun. And, oh yes, she will teach you how to read and write at the college level — something she knows from experience having taught at some of the country's top universities when she was a graduate student. In the summers where she has time (we got a new dog last summer so that took up a lot of our free time) she is working on researching and writing historical fiction.
My friends do a wide variety of things. Some work in archives. Some are on fellowships. Some have become teachers of various sorts in non-academic settings; some have become researchers/writers in non-academic settings (e.g. history for hire, or they work for NPR, or other options). Some work in universities, as professors in history departments, or sometimes even other departments. Their jobs involve teaching, researching, and writing. If you're a professor, you're also doing things for the university ("service"), like serving on committees and applying for grants and advising students.
So that isn't exactly comprehensive but I hope it offers up some of the wide spectrum of what it means to be a historian. The standard definition is "someone at a university in a history department" but there are plenty of other venues as well. It's generally not lucrative, though, if that's what you're wondering, and jobs can be hard to come by. It is not lazing about reading books all day, or even writing all day. But you have a lot of autonomy in your work for the most part.
This no doubt changes with what age one is, one stage one is in the overall academic lifecycle. The degree of writing, teaching, administrative work, etc., are all affected.
My mum is an Oxford Don in Modern European History at New College, so I am getting all of this from her.
Most of her time is taken up with tutorials and the like. She supervises theses and has to do the admissions to the college every year. Her position is kind of an odd one because she is one of the most senior fellows in her college, so she has certain responsibilities towards its running. As a special thing, a couple of years ago, she had to be the sub-warden of the college, essentially running the place for a year along side all her teaching. With all her duties she does not have a lot of time for her own personal research, she has to snatch time here and there to do it. This means that any full book takes forever to write, her latest one on the Dreyfus affair took over a decade from the first trip to the archives to publication. She also has to give papers, lectures and write articles for journals like Past and Present.
My understanding, from hearing profs in my department discuss it, is that their jobs basically consist of three parts: research/writing, teaching, and service. They pretty much seem to like them in about that order.
For many people, the opportunity to conduct original research is why historians do what they do. You identify a particular issue you'd like to explore, hopefully one that can make a contribution to the field and is at the same time relevant in some way to today. Once you've got that, you begin the actual research process, which is necessary to better understand the ins and outs of your topic. This might include doing a survey of the literature, which means you're scoping out what other historians have already said on the subject. This will help you narrow your focus and be able to identify the specific aspect of the historical issue you want to work on. Now, though, you have to become an expert on that issue, so you have to do primary source research. This can take various forms, depending on your field. Archival research is probably the most common, which involves spending time looking through archives for primary source material that relates to your particular historical question (I am still just a PhD candidate, and so consequently still really enthusiastic about archival work - it's like you're being a detective of the past, trying to track down clues to solve your historical problam, and simultaneously you get to glimpse some of the behind-the-scenes action that precipitated well known historical events). Alternately, you might also do some work in archaeology or oral history, to name two other common forms of research.
Writing is the flip side of research; once you have all of this great information, you have to tell people about it! So you need to write it up and then publish it. Lots of academics, not just historians, have a hard time with writing. One book that has helped me a lot by making me make a routine out of it (although the title is ... inaccurate at best!) is Joan Bolker's Writing Your Dissertation in Fifteen Minutes a Day: A guide to starting, revising, and finishing your doctoral thesis (New York: Holt Paperbacks, 1998). Getting your research written up is just the first step, though; in order to advance to get a great postdoctoral fellowship, or, after that, tenure and other history swag, you have to find a venue to share your work. Often these are journals, otherwise if it's a book-length manuscript, you aim for an academic press.
Teaching is also a big component of being a historian, even if you don't love it as much as you do research. Essentially, depending on the class, you might give a lecture to a couple hundred students, lead a seminar of fifty upper level undergrads, or facilitate discussion in a 20 person tutorial. This means you prep course materials, including maybe writing narrative-based lectures, manage the class, and either do the marking or have TAs who do it for you. Sometimes you also might agree to supervise a graduate student who is conducting their own research, which you would then facilitate. Teaching can be really rewarding; it seems to depend how interested the prof is in doing this, and how much they invest in the process.
Service includes any number of things that help promote the department. You might give a public lecture, do some outreach to local high schools, serve on university-wide committees, help in the hiring and tenure approval process, organize events with graduate students, do some community engagement work, etc. I've heard lots of grumbling about the demands this places on profs' time, particularly those who still haven't got tenure, who need to work really hard out of the gates to prove they are worthy of sticking around the department.
I've also heard some profs say (complain?) that the workload is 50% research, 50% teaching, and 50% service, implying that the department expects a lot from you. But, if you're really passionate about the past, and you can at least tolerate the idea of teaching and doing some departmental service, it's a great gig.