Lots more research, Emily. In addition to AW, you'll find some crossovers with the resource names above by checking out Writer Beware, Preditors & Editors, Piers Anthony's 'Hi Piers' blog, and the publishing blog 'Making Light'. (There are many others, these just come to mind now.)
Be cautious of publishers and agents you find advertised in writers' magazines. Some are quite legitimate and reputable - others, not so much.
Google 'Publisher name, complaints' to see if anything shows up in search engines.
If you want to drill down deeper on a publisher that has already released books, fill in their name on the search bar at
www.salesrankexpress.com, and see an estimate of their Amazon sales rank. The higher the number, the lower the sales; anything with 1,000,000+ Amazon rank is probably selling in the single digits per year. If a publisher has too many of these low-selling books, they may not be effective at marketing what they produce.
Amazon isn't the only market, of course. Sometimes publishers say they're selling like gangbusters through their own website portal. You can get an estimate of how popular their website is by pasting their website address into the search window at Alexa.com, a large internet analytics site. If not that many people are visiting a publishers's site, some of their 'sales' may be coming from their own authors purchasing copies to hand-sell. It's not a bad thing for authors to do their own promotional sales, but beware publishers who want to make you do it all AND take part of your royalties anyway. Especially if they want you to pay upfront fees, too, or levy after-publication purchase requirements.
Look up their authors on social media and see what they post about their publisher and their writing journey. Writers can be chatty people, and their comments can reveal satisfaction, anger, or confusion if you read carefully.
Look up their owners and editors on social media, to see how they handle themselves in public.
Look up a publisher's authors on Amazon and see what else they have published: either before, concurrently, or after their association with the target publisher. If too many authors show signs of falling for notorious vanity publishers and other scams, it's a fair bet they'll do so again - and you may need a closer look at the target publisher's business model.
Likewise, look to see if an author has too many gushing 5-star reviews on Amazon, B&N, and other vendors - and pay close attention to reviewers' names. Sometimes an author's friends and family post reviews. Their 'agent' might post reviews, sometimes not even under a sockpuppet name. Authors will even post reviews of their own book. In short, a lot of these tags can indicate a book that may not actually merit its glowing praise...or is at least not reaching a market beyond its author's friends and family.
Find out where the publisher is registered as a physical business, and check city and state court records to see if they've been involved in any legal action. Check their state's Corporation Commission or the equivalent to see if their business filings are in order. Google the names of the publisher's owners/organizers to see if they've had other businesses.
There are people here on AW who will often do this as a matter of course, while researching a publisher. Knowing how to do it yourself is a good skill.
When another writer mentored me in 2010, she said, "How long did it take you to write your book? Two months? A year? You should spend at least a month researching publishers, otherwise you're just blindly throwing darts and hoping for a win."