Unfortunately, this is a huge question. So, I'll provide a generic overview answer from a few sources.
First, here is the Wikipedia article describing Emerging churches (the Emergent Movement). It covers a lot of ground.
A simpler overview of their principles can be found in Emerging Churches: Creating Christian Community in Postmodern Cultures by Eddie Gibbs and Ryan Bolger (Baker Academic, 2005)
Emerging churches are communities that practice the way of Jesus
within postmodern cultures. This definition encompasses nine
practices. Emerging churches (1) identify with the life of Jesus, (2)
transform the secular realm, and (3) live highly communal lives.
Because of these three activities, they (4) welcome the stranger, (5)
serve with generosity, (6) participate as producers, (7) create as
created beings, (8) lead as a body, and (9) take part in spiritual
Finally, there's an interesting Christianity Today article about it here.
Trying to give much more detail than that would lead to a book deal.
As far as who identifies themselves with that movement, it seems that they do have community that clearly defines themselves as "emergent". (here).