You design a transfrmer by selecting a suitable core, usually silicon steel laminate for mains transformers, the primary is then calculated, this done so that the magnetic field ustilises the core fully but doesnt saturate it, then its just a matter of turns ratio and wire size for the secondary.
You can get transformer design calculators of the net.
If you want a particular transformer a good way to start is to get a transformer kit with a pre wound primary, you just wind the secondary for the voltages and currents you need, equations come with the kit.