Kyle at RightWingWatch explains:
For all the recent talk about the New Apostolic Reformation, one of the issues that has largely gone uncovered is just what it means to be an "apostle" within this movement. I have recently been reading C. Peter Wagner's "Apostles Today: Biblical Government for Biblical Power" in which he helpfully sets out his definition:
An apostle is a Christian leader, gifted, taught, commissioned, and sent by God with the authority to establish the foundational government of the church within an assigned sphere of ministry by hearing what the Spirit is saying to the churches and by setting things in order accordingly for the growth and maturity of the church and for the extension of the kingdom of God.
Wagner also explains that there is no such thing as "self-appointed apostles" because all apostles are appointed by God. But that creates a bit of a dilemma for those trying to determine who are actual apostles versus those who are false apostles and so Wagner offers a rather ingenious way to tell the difference:
God's decision to make an individual an apostle must be recognized and affirmed by real people. If someone says, “God has called me to be an apostle,” but no one else agrees, then I have to doubt whether that person has accurately heard from God.
Now, if that logic seems rather circular to you, Wagner also offers up a list of "12 characteristics that are displayed by many (if not most) apostles," though he is careful to explain that not all apostles have all 12 characteristics.
But, as a basic rule of thumb, seeing Jesus, performing miracles, suffering persecution, casting out demons, and fighting witchcraft are among the characteristics that a NAR apostle might posses:
1. Seeing Jesus personally. Of course the original 12 saw Jesus, but so did Paul...
2. Performing supernatural manifestations such as signs and wonders. ...
~snip~
For the rest:
http://www.rightwingwatch.org/content/understanding-apostle-new-apostolic-reformation