I generally provide little to no biographical information about the author, focusing on the text itself. I like a Reader-response approach, but what I want students responding to is the text alone (and their experience with it). I don't want students to worry too much about the author's identity or biography (with some exceptions). In some cases, if students ask questions about the author, I can provide them nothing because I know nothing (other than that they write in English, and perhaps a general idea of when they wrote). I do provide some cultural and historical material, but only when it is directly relevant to the text itself.
The specific context today was Robert Frost's "Home Burial." While teaching this poem, I often talk about ways of dealing with death: the different ways individuals handle grief, the rituals we construct surrounding death, etc. A student raised the issue of gender roles in the poem, and I'm open to that exploration (though in this poem, I didn't want gender roles to define the different ways the husband and wife grieve). But for some reason when it was pointed out that the poet was a man and could be slanting perspectives of the characters (which is true), I found this a tremendous distraction from the text itself. The wife in the poem has lengthy stretches of straight dialogue where she is able to express what she thinks and feels. If we get hung up on discussing how a male author constructed those words for her, then we aren't taking the words of the text on their own merits, and I don't think we're reading the poem well.
I don't think I can formally call what we do in my literature classes New Criticism: I'm far too willing to bring up extra-textural material if I think it offers insights into the text (or if I think the text offers insight into extra-textural material). But in my decision to forgo authorial biography almost entirely, and my insistence that students respond to what they see in the text itself, I'm certainly incorporating the ideas of New Criticism into the classroom.