This is a unregulated supply for low power circuits. You may be able to regulate the outputs with zeners or small regulators like 78L05.
The transformer can be hand wound in a mini ferrite pot core. you can use 2N2222 or any other fast transistor. The transformer should have 1KV isolation. The dot polarity of TR1 should be properly observed, else it may fail to oscillate or give output.
Diode should be fast recovery type, for less than 100mA use 1N4148. transformer, pri-20-20, sec-60-60, a SWG-AWG to suit the current you
Circuits using only discrete devices
design for, any fast switching transistor would work, no regulation, use regulators like 78L12 if you want, circuit like multivibrator used for flashing LED lights.