Here is their Duotrope Page.
Mark your calendar: Their regular submissions are from June 1 - November 1. They also have four contests with November 1 deadlines. They are the Edwin Markham Prize for Poetry, the Gabriele Rico Challenge for Creative Nonfiction, the John Steinbeck Award for Fiction and the Mary Blair Award for Art.
What it costs to submit: Regular submissions have no fee. The contests cost $20 to submit and have $1,000 prizes aside from the Gabriele Rico Challenge for Creative Nonfiction which has a prize of $1,333.
What to submit: Five poems or one piece of prose up to 5,000 words.
What they say of themselves:
"For over 150 years, Reed Magazine has published the work of artists such as Ursula K. Le Guin, Robert Hass, T.C. Boyle, William Finnegan, Stephen Dixon, and Don George—artists whose narrative voices persist beyond print, whose imagery lingers in our minds, and whose language challenges us to think, to do, to be part of the creative legacy of our time.
Reed Magazine is for the truth-speakers:Poets who reach universality through the chocolate chips in a breakfast pancake; Fiction writers who craft characters that could walk off the page and into our living rooms; Nonfiction writers, whose essays make large what was small; And visual artists, whose work illuminates all these stories and others–the political, the social, the cultural history of humanity.
No matter your medium, the staff at Reed Magazine wants to hear your stories."
Read some of their stuff if you're hearing about them for the first time before submitting. They are a tremendous journal.