One method is to do an online search for the title of their book(s) and of their authorname. Another is to set up a variety of Google Alerts for their book title, also for some distinctive phrases used in their writing.
Osborne Clarke suggests some practical ways to respond to infringement.
I can say with reasonable certainty that, if a so-called online library is lending a "Rowena Cherry" book--for instance "Knight's Fork by Rowena Cherry" to subscribers in any digital format, that online library has no right to do so, because I never gave permission --and explicitly refused permission-- for any of my books, except "Mating Net" by Rowena Beaumont Cherry (which is published by New Concepts Publishing), and the hunk cover version of "Forced Mate" by Rowena Beaumont Cherry which was published by NBI, to be released in ebook formats.
Did you notice that? A lawful digital copy of my work is by "Rowena Beaumont Cherry". Any ebook by "Rowena Cherry" was illegally created and illegally sold.
However, if the (alleged) pirate site uses a privacy service, and the privacy service is the only link provided on the (alleged) pirate for any kind of contact at all, an author is within her rights to contact that privacy service to complain vociferously and repeatedly.
But... do not create an account. In my opinion, Congress and the Administration and the Copyright Office make a serious error when they agree that it is lawful for a site such as EBay to force authors to join its VERO (verified rights owner) program in order to complain about copyright infringement.
Why should a creator who is being ripped off be denied the right to send a DMCA notice, as prescribed by the Digital Millennium Copyright Act, and forced instead to subscribe to a site or become a member of a site?
It's like being forced to purchase a product one does not want or need. Only it is worse.
The trouble with joining any site or service, (apart from the possibility of having to pay them) is the Terms of Service. One cannot join (even for the purposes of asking them to cease and desist from piracy or facilitating piracy or profiting from piracy) without agreeing to their TOS.
Have you ever read TOS? Try it sometime. Any site's TOS will do. Do judges and lawyers and lawmakers read TOS? Usually, part of what you agree to is that you give up the right to sue them.
How's that? A site like EBay or Google may protect alleged copyright infringers, and give the alleged copyright infringers the ability to profit from alleged piracy, but in order to send a takedown notice, the ripped off author is forced to promise to indemnify the host and patron of the alleged copyright infringers. That does not seem right to me.
On the other hand, there are many online "subscription libraries" that one suspects do not have the books they claim to have. They may only want your credit card information.
Stay wary, my friends!
All the best,