from PyQt4.QtCore import QVariant
from qgis.core import *

inLayer = iface.activeLayer()
provider = inLayer.dataProvider()

# add field
field = QgsField('test_field', QVariant.String)
inLayer.startEditing()
provider.addAttributes([field])
inLayer.updateFields()

# commit
inLayer.commitChanges()

layer = iface.activeLayer()

name_column = "new_column"

layer.dataProvider().addAttributes([QgsField(name_column, QVariant.String, "VARCHAR")])
layer.updateFields()