  We consider knots equipped with a representation of their knot groups onto a
dihedral group D_{2n} (where n is odd). To each such knot there corresponds a
closed 3-manifold, the (irregular) dihedral branched covering space, with the
branching set over the knot forming a link in it. We report a variety of
results relating to the problem of passing from the initial data of a
D_{2n}-coloured knot to a surgery presentation of the corresponding branched
covering space and covering link. In particular, we describe effective
algorithms for constructing such presentations. A by-product of these
investigations is a proof of the conjecture that two D_{2n}-coloured knots are
related by a sequence of surgeries along unit-framed unknots in the kernel of
the representation if and only if they have the same coloured untying invariant
(a Z_{n}-valued algebraic invariant of D_{2n}-coloured knots).
