Which form is correct?
Do you know the guy who I talked yesterday with?
Do you know the guy who I talked with yesterday?
You can also omit the "who."
(If The Parser sees this, he'll also tell you that "whom" is technically the correct form there, but few people would use it.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.