There have been several discussions on professional history here that should be useful, but at the outset we may want to define what a professional historian is. Does a secondary school teacher who performs and publishes primary research count? What about a museum docent?

If you have in mind traditional tenure-track faculty positions at universities, you will need a PhD in history or allied discipline.

Postgraduate

This is a pared down version of the process for the United States; although Western Europe shares broad similarities, every country is different, and oftentimes institutions have remarkably different processes.

To apply to a graduate program you typically need to be in your final year of or completed with your bachelor's, furnish three letters of recommendation, a personal statement, and provide a writing sample. Some candidates apply to M.A. programs first, and upon completion of the Master's continue onto the PhD. Many programs require the GRE to be submitted as well. Your undergraduate degree does not need to be in history, but your writing sample should be your strongest text that shows your skills, and your personal statement should show that you have seriously thought your research question. You don't get a degree in 'American History' or 'Indian History' so much as a specific research goal: perhaps you are interested in the relationship between American fin-de-siecle anarchism and robber-baron industrialists, or the influence of 1857 on British colonial administration, or so on.

PhD programs generally accept applications in the fall and return admissions decisions in the spring. Once you are admitted to a PhD program, very nearly all American departments offer a graduate stipend, though this varies widely; in general, they are livable, but not lavish. Your program can take anywhere from four to twelve or more years, but six or seven is about the average for history.

Faculty

Once you complete your PhD, you can apply to faculty jobs, though many candidates who ultimately obtain a TT position are initially employed as adjunct roles or postdocs for several hiring cycles. There are more PhD graduates than there are TT positions, and every year more graduate: so the PhD graduates that do not secure a faculty position end up leaving the academia, or staying in contingent roles.

The AHA produces jobs reports annually, which show that there are around twice as many history PhDs as there are advertised jobs in history--when you consider the PhDs who did not secure a job in the preceding year, the difficulty of securing a traditional job is quite apparent.

The graduates who do go on to tenure-track roles have differing tenure requirements based on institution, but for schools with research expectations history is generally a "book discipline." Many faculty turn their PhD dissertation into their first book.

For the graduates who leave the academy, they go on to business, nonprofits, museums, further postgraduate programs--and while they no longer perform scholarly research for money, they have the skills and credentials of a professional historian. If someone has a PhD in history but works in university administration, counseling graduate students on non-academic careers, are they a historian?

Alt-academic careers

I hold a broader view of what makes someone a historian than the career track I sketched out above. I recognize the value of academic credentials but don't view them a sine qua non for "historian"--there are some pretty shoddy PhDs out there, while there are some phenomenal historians who did not attend a postgraduate program in history. The skills that make someone a historian are probably best learned in an academic setting (otherwise we wouldn't have forums like /r/badhistory), and institutional affiliation is certainly valuable in pursuing scholarly research, but once you have those skills and connections you can pursue research independently. The growth of 'independent scholars' attests to the importance of non-affiliated scholars.

To you, 'historian' may not necessarily mean research and interpretation, but dissemination of scholarship in local museums, non-profits, living history institutions, and the like--this work is very important for communicating history in a more public way than scholarly books that are oftentimes cloistered within disciplines, and when done right can really bring the value of history into the public eye.

It's worth drawing out the opportunity costs of graduate programs as well; M.A. programs you must generally pay for, while PhD programs in the US pay between $20,000 and $35,000 per year. If you enter after you complete your undergraduate degree at 22, and take seven years, you graduate at 29 and enter the professional world without the experience and salary growth that your colleagues might have. /r/AskAcademia is a good place to look at finer discussions on academic history.

By reading scholarly texts (and eschewing 'popular history') you can understand the products that professional historians produce, and see if this is what you want to pursue. Once you develop research questions and situate yourself methodologically, I think the barriers to scholarly research are difficult but surmountable.

In my case I went to a graduate school that had an Archival Management program built in. I had volunteered at the college archives as an undergrad and thought it would be good to have a few options.

My taste for academic history faded pretty quickly but after graduating I did contract work with a local (NYC) archives consulting group. My advisor at NYU dropped my name to a headhunter and I got hired for a corporate archives job which was absolutely not on my radar.

I ended up doing 2 years there and 10 years as a corporate archivist total before transitioning to tech where I am now. There's a lot of weird contempt within the archives world for people in corporate work but it was an excellent niche for me and frankly paid better. It's been a bit rough as a lot of places cut their (already miniscule) archives budgets but it's a great way to keep involved in history even if academics isn't for you.