I'm trying to learn how to make these circuits but have no clue if I'm on the right track?
You have a common bridge rectifier and bulk storage capacitor, this is your unregulated supply, by controlling the transformer turns you can control what this voltage is, 

You would ideally size the voltage, or the capacitor size to ensure with your known load it never falls below your regulation "Dropout Voltage", e.g. a linear regulator trying to output 9V might misbehave when its input falls under 10.5V

The exact way you make the regulators are up to you, its likely to involve active devices e.g. transistors and diodes / zener diodes to give you a starting point for what to look for

As to the nominal value, power and voltage rating, each component has a power and a voltage rating where if exceeded will damage the device, e.g. a 1/4W resistor can only handle a quater watt of heat, go much above this and it may de-solder itself off a PCB, 

Voltage rating would more apply to capacitors, the lower the voltage rating, the cheaper and smaller, the rule of thumb is give yourself a headroom of atleast 20% on the voltage rating, so find the maximum voltage you expect, and round it up to the nearest normal value atleast 20% higher, this is headroom for things like spikes and surges on the mains power

Nominal value would be either average voltage / power or possibly the specific component values. depending on context.