I had my book reviewed by people who are interested in the topic of the book. Now interested in reviews by professional book reviewers. What is the appropriate way - directly approaching potential reviewers or submitting the book details somewhere online?
You need to follow a lot of blogs by other professionals in the field. Comment on their blogs, reply to their tweets, engage with them. This way you will build credibility, and the other professionals will get to know you.
Once your name has some "brand" awareness, then you can ask others to review your book. It would help you if you review books by others too.
Of course, this whole process may take a few years, as it takes years to build credibility. Unless you are well known in your field, you may not get many reviews from professionals.
I have no direct experience in getting professional reviews, but I've been reading about the topic lately. Here's my understanding:
Some major newspapers and magazines do book reviews; most have public submission guidelines. Typically, as described on this page for the New York Times, the submission is expected to be from a publisher a few months before the book is published.
You or a publisher's publicist can also contact book reviewers directly. Jacqueline Deval, in Publicize Your Book, describes such a submission as including either a letter to the reviewer or a press release, and a copy of the book itself.
A third option is to contact someone you think would be interested in your book and ask that person to write a review and submit it to a publication in the same area as the book. (I've been asked to do this, for example.)
My impression is that it's hard to get prominent reviews of a book without doing a lot of legwork, unless you're already well known. But it seems to be doable.