With great difficulty.
There are a lot of factors at play, some of which are dependent on
characteristics of the materials involved that aren't always easy to pin
down. Moreover, how you use the transformer in your circuit matters.
Finally, for some applications the efficiency doesn't matter nearly as
much as other things; usually bandwidth or fidelity of reproduction.
Factors that I know of are:
The resistance of the windings,
the resistivity of the core material,
the thickness of the laminations (if any),
the nonlinear magnetic properties of the core material,
the overall shape of the core and windings
I'm sure there's more.
I suspect that even in this day and age of high-falutin' computerized
finite-element analysis, you'll still find that in practice anyone who
can build you a transformer and have it possess the correct efficiency by
design is someone who has designed and tested dozens or hundreds of
similar transformers and is leaning on a wealth of practical information,
rather than analysis from "first principles".