  We study $3$-dimensional Ricci solitons which project via a semi-conformal
mapping to a surface. We reformulate the equations in terms of parameters of
the map; this enables us to give an ansatz for constructing solitons in terms
of data on the surface. A complete description of the soliton structures on all
the $3$-dimensional geometries is given, in particular, non-gradient solitons
are found on Nil and Sol.
