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As always, I agree with Zen . It isn't so much about about a certain process as it is about a bit of research and healthy dose of common sense.
If someone approaches you to offer publication/representation, be wary. That's not how editors and agents usually get new stories/clients. They are simply too busy with all the material being send their way. People come to them.
It can happen, but it will usually be because of your previous publication record or your already established connection to said editor/agent. Always ask you self in a situation like this, how do these people know about me and my writing? What do they stand to gain from accepting your story? Be a bit cautious.
Whether they approach you or you're considering submititng to the agent/editor, Google is your friend. Search for their names and try searching for them in combinations with words like "scam" or "controversy". If they are known scammers, it usually doesn't take a lot of time to find the information. (For magazines, especially SF&F magazines, I recommend using a database like The Submission Grinder. They are quick to remove magazines from their listing if they have a bad reputation or shady contracts.)
If you don't find any red flags immediately, dig a little deeper. Not all scammers are well-known yet, and it's not only scammers you should be wary off. You want your future editor/agent to be a good fit as well. Besides, practically anyone can start up a micro publishing house or their own literary agency, and that's fine, but an amateur for-the-love of it publisher/agent isn't necessarily what you're looking for.
If you want more than just to see your book being published, research what the publisher/agent's track record. What other authors do they publish/represent? Can you find their clients in actual bookshops?
If you've gotten this far, decided to move on, and received and offer, read the contract thoroughly before signing (should be common sense) and, again, research. Does it look like the kind of thing you would expect from a reputable publisher/agent? Does it look like a standard contract (organisations such as SFWA have ones you can compare with)? Does it have weird clauses or requires you to pay them instead of the other way around?
Some literary magazines or agents have reading fees, but generally the money flows towards the author.