The easiest way to deal with a dishonest or illegitimate publisher is to avoid them in the first place.

Know your rights

1. Until you sign something, you own your copyright. You may share ownership of a work with coauthors, but only you can sign your share of that ownership away. A publisher's leverage rests entirely on securing your copyright from you; until you transfer your copyright, you have the leverage. Resources like the Authors Alliance or SPARC can help you to learn about what that leverage means for you.
2. Don't take an email from an unfamiliar publisher or journal at face value. Use a checklist, like Grand Valley's or DOAJ's, to investigate and evaluate before making any commitment.

Raise your awareness

1. ​Do your homework when considering an invitation to publish or serve as a reviewer. Who is it that's asking for your scholarship or your time, and what are their practices? Don't wait to find out until it's too late.
2. Pay attention to who publishes the journals you're considering; reach out to colleagues listed as authors, editors, or reviewers before you commit to anything to verify their affiliation with the journal or publisher. An illegitimate publisher will often list people as editors or reviewers without their consent.
3. Review the easy guidelines at Think. Check. Submit.
4. Learn how to critically read a call for papers from an unknown outlet. See, for instance, an example from Governors State University Library.

Once you're on the hook, disentanglement can be extremely difficult. If you realize that you have been taken in:

Stop

1. Withdraw your article and/or withdraw your name from reviewer lists
2. Do not pay any fees, especially once it becomes clear that the operation is illegitimate. Once they realize they're able to get money out of you, they're only going to want more.
3. Do not sign anything and do not transfer your copyright.

Speak out

1. Contact University Counsel. If a publisher has infringed on your copyright – published your work without your consent, for instance – consider litigation.
2. Contact the publisher. Demand to be removed from the editorial board, list of reviewers, etc.
3. Tell others. Predatory publishers count on their victims staying silent out of embarassment in order to continue their operation. Save your colleagues from falling into the same trap.