Bob, the answers are easy: You do your homework.
You research a publisher or agent before you ever query them. You determine if an agent has made legitimate sales and plenty of them, and who their authors are. You determine if a publisher is legitimate, pays royalties, and seeks nothing but the manuscript from authors.
How do you research? Visit large bookstores. Note titles, authors, and publishers of the books in your genre.
Get online and try to determine which agent sold each book. (Search “Full Title” + agent. Also try “Author Name” + agent.) You can find other agents seeking work in your genre through “Writer's Market” and “Literary Marketplace” (US) or “Writers’ & Artists’ Yearbook” (UK). Check the publisher listings, too, which will include “agented submissions only” or not. (Maybe you don’t even need an agent.)
Research each agent. Find websites with career history, sales, personal bio, blogs, AAR membership, etc. Determine whether they prefer email or regular mail for queries. Figure out who’s a good fit for you. Don’t be afraid to aim high. The worst that can happen is they say no. Your research should include a visit to Preditors and Editors.
Write a one-page query letter, tailoring it to individual agents or publishers based on the information you got from research, and send it to the few agents you'd most like to represent you. If the query letter is really good and you've done your homework well, at least some will ask for a partial or full manuscript. If none does, rewrite the query before sending out the next batch.
Remember, reputable agents charge the author NOTHING up-front. Some agents may deduct the costs of doing business (copies, mail, phone) from your first check, but nobody legitimate needs any money to get started.
Legitimate agents and publishers who stole your work would face charges which would drive them out of business in short order. They would not risk all that money-making potential to steal the work of an unknown writer. It would cost them way, way less to buy the rights to the book and offer you royalties.
BTW, Arthur Levine is legit, as far as I can tell. As J.K. Rowling's American editor, he's undoubtedly getting every fantasy-and-magic wannabe, so the competition may be daunting.