Business card is good. Editors do not want to load their luggage up with manuscripts or even parts of manuscripts.Have you asked your agent about this? If the agent knows any of the editors, see if the agent can set up a meeting, maybe even a meal together. At the very least, the agent could introduce you to the editor.
A good thing to do for homework is to find out what works the editors edited and say something complimentary about them. (You may need to find out which editors are going to be there, and then find out what they've edited. You may also need a scorecard or a cheat sheet, to make sure you don't get one editor confused with another and offend the editor you are talking to.)
Best thing is to make yourself known to an editor, and then when you send something, you can refer in your cover letter to having met the editor.
As for approaching one that's read your work, you could introduce yourself and thank them for reading your work.
The idea is to make contact, keep it short and sweet, and unless you have arranged in advance to take up some of the editor's time, leave it at that. Editors use big conventions to conduct business and they appreciate people who make it easy for them to do that.