All magnets exists as dipoles, there are no discovered monopoles. There are two main models for understanding the Moment of these dipoles.
Moment
The magnetic dipole Moment is given by:
Formula
Magnetic Dipole Moment
Terms
The direction of the magnetic moment, is given by the Right Curl Rule
Hypothetical Monopoles - Gilbert model
In the Gilbert model, hypothetical monopoles are position in the same configuration that an Electric Dipole would be, i.e. one monopole is north pole, while another one is south pole.
Coil of Wire - Ampèrian Loop Model
Since a loop of wire produces a Magnetic Field, a magnetic dipole can be modelled as a loop of wire. The orientation of the poles depends on the direction of current flowing through the loop, but there always exists a north and south magnetic pole