They send fake checks, and they ask you to send the money to newspapers that don't exist. Then you get nailed for passing bad checks and they keep the money when it arrives.

It's a convincing scam because:

They don't ask for much info, just mailing address and email.
They don't promise incredible money or get get rich quick ideas, just 400 to 800 a week.
They have their own website and will answer your emails.