In this day and age, with more and more people going the self-publishing route, I'd be interested in experiences from/opinions about how to go about having your self-published book properly peer-reviewed.
In mathematics, traditionally, and I think currently, very few books are reviewed at all in any serious sense. One possible sense would be "critical appraisal", and this is rare: a handful of books is given serious reviews in the Amer. Math. Soc.'s "Bulletin". The other possible sense of "peer review" is in a sense adding something to one's CV for jobs, tenure, promotion, grants. Almost by definition, this never happens. That is, "refereeing" is done for the conventional journals, whether paper or electronic, and referees are solicited by the editors, for papers submitted to that journal. The "valuation" of books is typically done not via "reviews", but by the status of the publishing house, and the status gain from publishing a book is probably less than a small paper in a medium-status journal. Thus, in particular, self-publication confers none of that cachet. And I'd wager that self-publication would compromise "review" in the sense of appraisal, as well, because other publications would have higher priority for the reason of status.
(I do hope things improve, but I do think this is the current state, in mathematics.)
Edit: As examples of "self-publication", disregarding the "peer review" idea entirely, a certain number of relatively senior (and not only!) people put book-like items on-line at their web-sites, often at universities. I heartily endorse this (and have been doing it myself for quite a while!) However (?), this appears to confer even less status than "books" published in physical hard-cover, I presume because there has been no hurdle of sufficiently-impressing publishers (who do ask opinions before "consenting" to publish).
The more legitimate issue of "(peer?) review" to ascertain correctness, or helpfulness, etc., I think has so few precedents that little is happening. First, Math Reviews has no procedure in place to review such things, and it doesn't happen. Second, there appears to be considerable reticence to cite such things, even in stable situations, for a variety of (not entirely sensible) reasons. Third, while one might imagine that on-line, thus, dynamic, documents could be more reliable, by virtue of being correctible (indefinitely!), this actually disturbs/perturbs many people... Further, third(b), disappointingly to me, very, very few people have ever given me any feeback/corrections about my on-line stuff, or even asked for clarification (in some cases leading to correction or, anyway, better writing). I can imagine that some of this is politeness, or respect, which is understandable.
But, I might claim, the real "problem" is lack of precedent. The "refereed journal" model is 150+ years old, and itself depended upon evolution beyond the "reading before the Academy" 200+ years ago when printing itself was a non-trivial matter, etc.
Thus, rethinking the action-oriented sense of the original question: since "self-published" ought mean nothing, really, in today's context, apart from the fact that it doesn't have a "prior" approval from status-conferring entities... to "get an expert opinion" one ("gosh, let's just try to think clearly for a sec!" :) would send th'thing to (web-obtained?) experts, asking very politely whether they'd be so kind as to offer critical remarks... and as a very polite secondary question, whether they'd be willing to be quoted in such remarks.
(This has led me to thinking that the difficulty in quantifying "civility" and "politness", especially between different generations (if only in convention and usage), potentially causes substantial difficulties in on-line forums, and/or "stack-exchanges", and or . Not that I think high-status entities have a "moral" superiority, which is the stereotypical exaggeration-to-disqualify, and which is a popular (mis-) interpretation of that elite, but that experience can be worth something, and that something is not easily acquired by any other means.)
The question is extremely vague. The OP could be a professor of creative writing who has written a novel, a math professor who wrote a calculus textbook, a sociology professor who wrote a monograph on water rights in 19th-century Oregon, or a physics crank who wrote a book proving Einstein wrong.
In the case that this is research: --- In some fields of academia (e.g., literature, sociology), it's normal to publish books and monographs on one's research, and these are considered professional pluses (e.g., for tenure). In other fields (such as physics), this is not normally done, and a book is not a feather in the author's cap. If this is a field where research often is published in book form, then the way to get peer review is to submit the book to publishing houses, whose acquisition editors, if they think the proposal/manuscript has possible merit, may try to get academics in the field to review it. Yes, the acquisition editor is a gatekeeper. No, there is no way to get around the gatekeeper and convince random academics that they should read a manuscript. There's a reason that acquisition editors are paid money. It's because the job they do is dreary and thankless. Random academics are not going to wade through a slush pile for free.
In the case that this is a textbook: --- There is a model that has been going on forever, which is that you distribute the book to your students via the best available technology of your era (quill pens, purple mimeos, internet), hone the book over years of teaching the same course over and over, and then, finally, send it out to publishers. A typical modern exmaple of this model is that Sean Carroll posted his textbook on general relativity on the internet here in 1997, and in 2003 it was published in dead-tree format by Benjamin Cummings. If, like Sean Carroll, you're ethical, you make sure that your own students can get the book without paying you money. If you succeed in getting the book published in print by a traditional publisher, you can usually, if it's important to you, negotiate a clause in your contract allowing you to keep the book online for free.
Some people do self-publish textbooks as an alternative to traditional dead-tree publishing (rather than as a preliminary to dead-tree or a last resort after failing at dead-tree). A few of these projects are successful in the sense of gaining adoptions by other professors. This path does not involve peer review.
I think "peer reviewed" and "self-published" don't go together. You get a piece peer reviewed to provide and objective, 3rd personal appraisal of the work. You self-publish because you couldn't get published anywhere else. Everyone will automatically assume that your book wasn't good enough to get published somewhere "real" if you self-publish.
Some quick comments to explain my remarks above. They aren't intended as normative remarks (i.e. "Nobody should take a self-published work seriously") but rather as descriptive (i.e. "Whether it's right or wrong, people aren't going to take self-published work seriously.") Sure there might be exceptions, but I think it holds up as a general rule. Here's the reasoning behind that descriptive claim.
The reason to publish is to disseminate your ideas. You don't publish things intending for no one to read them. Therefore, readers and other evaluators of your work, like tenure committees, grant agencies, etc will assume that you are publishing your work in the "best" places you can, i.e. the journals that are read or cited the most or with the publishing house with the best reputation in your field that you could get published in.
There are two reason for peer-review. First, the criticism of informed peers helps improve the work. Second, because the peer review process provides an independent evaluation of the quality of the work. Peer review has a signaling function within the academic community--it says that you aren't a crank. This second function is hugely important. There is too much to read and cranks are always pushing new nonsense all the time. Nobody has the time to sit down and give a careful, thoughtful evaluation of every piece that appears relevant to their research question, so they use heuristics to sift out the nonsense. Peer review is one of those heuristic filters.
Now, if you already have an established academic reputation, maybe you can get a readership without the peer-review heuristic based on your prior work. But then you'll be missing out on the other benefit of the peer-review process, namely the helpful criticism of your peers and an objective 3rd personal appraisal of the strengths and weaknesses of your work by an editor. You could hypothetically get your friends or acquaintances to review your work, but (i) given the time constraints most faculty face, I think it'd be hard to recruit quality referees for your self-published work; (ii) their reviews won't be blind; (iii) there won't be an independent 3rd party editor who makes the final call based on these reports. If you are self-publishing you are the editor and the author, hence you have a conflict of interest and can't give an objective evaluation of your own work.