I wrote a paper, which I would like to submit to a convention. I've never written a paper before. I'd like it to be thoroughly reviewed, not to say edited, before I submit it. I'm willing to pay for a reviewer. Where can I find a reviewer? The orientation is mathematics related to computer science (specifically formal methods).
(Academic editor/copy editor here, though not in your field)
A review will happen after you submit: the publication/conference will check that it fits their vision, which may mean a thorough technical review, and may not, but you don't pay for it.
What you can do to improve your chances is to employ an editor if you don't have access to either tutors or peers you can exchange work with. Many freelance editors/copy editors will be happy to work with individual authors. The best ways to find them are through word-of-mouth in your department, if you have one or through reputable organisations like the EFA (Editorial Freelancers Association or the sfep (Society for Editors and Proofreaders, UK-based). I'm also impressed with the overall quality of editors listed on the CE-L (Copyediting Mailing List) Freelancer directory.
It's still buyer beware, but you stand a better chance than hiring through a service that promises cheap and fast (but which does not necessarily provides the math skills).
Your best bet is offering a graduate student a lot of money. In most cases this is going to be an unpleasant job. In most cases, the paper will be some combination of incorrect, incoherent, and uninteresting, but the author will usually be very resistant to hearing that. (I don’t know you, hopefully this doesn’t describe you or your paper, but whoever you hire also isn’t going to know you or your paper.) So you’re going to have to offer a lot of money to compensate and offer it to someone who doesn’t have a large salary. Something like $100-$150/hour with the first two hours paid up front would probably be enough for a graduate student to overlook that it’s likely to be an unpleasant job.
Well, the first step would be to get through the basic checklist yourself: is this novel enough; do I follow established order; do I cite the relevant papers (say 20-ish with at least some recent ones). If you are doing it on your own initiative, you have a blind spot regarding first point, believe your flow is better than what is in other papers and almost surely cite (and have read) far too few papers. You should fix that yourself, especially regarding citations.
Once you have basics sorted out, you should call anyone that could be somewhat interested to look at your paper. If you are a researcher in a field not very well covered by your university/faculty, you should find some people from the general subject (say someone from algorithms if you are writing about a novel sorting one). Most likely that will be a professor (that will usually delegate to his PhD student or a postdoc). It could be a friend that went for PhD in a somewhat related area. Don't expect a thorough review, but a lot of people are nice enough to quickly skim through what you wrote to point you in the correct direction for nothing more than a beer.
If you get a response that your approach seems OK and the paper doesn't need A LOT of revision regarding these basic bits, you have 3 main options:
Offer joint paper - they edit it to the best of their ability and get their name there. This is likely the best option for you, as having a name of someone relevant will increase your chances of acceptance, and it doesn't cost anything.
Offer money to review, as in Noah's answer.
Submit and hope independent reviewers give you some "fix XYZ" pointers. Even if you get rejected, this will help for the next submission. If you are unable to solve those comments yourself, revert to options 1 and 2. If comments are along the lines of "incorrect/pointless/trivial/...", options 1 and 2 again. Note that you will almost surely "burn" that particular conference/journal/... and will have to find another one. Plus your paper will be surely worse without assistance and will end up in a lesser journal/conference/...
If you want an editor who's checking only for English, there are plenty of options available, e.g. American Journal Experts (you can Google for more results as well). I have not used these services, but I did freelance for one of them in the past, and they do what they say they do: they edit your English until the manuscript is no longer being rejected for bad English.
These services do not review the content, however. If you want someone to review the content, you'll very likely have to pay for it. Your best chance is probably to approach someone who's working in the field of that paper - e.g. email graduate students in the field as suggested by Noah Snyder, since they probably have more time + more need for the money.
It seems that you are not in academia. If you are convinced that your work migh be publication worthy but somehow feeling an advice is necessary, then you could contact an expert, preferably in your area.
S/he probably won't edit your paper, but a general opinion is something less time consuming and you could get one. It really depends on the manuscript itself. A minimally known professors might receive garbage from outside, spanning from totally nonsense to rediscoveries. Not that I suspect your manuscript belongs to those categories, but perhaps you could have clarify why your question have raised.
For putting the paper in a final linguistically clear form then look for someone offering translation services and the like.
If you are in academia, then is not particularly easy to answer as the situation would point to an isolated researcher not fully aware of situation / not sure about his/het work.
I wasn't sure to answer also because review and edit can overlap but can be totally different tasks.