This is done using a RESERVOIR capacitor.
It is not called this because of its construction but because of its application.

In the UK the weather is very variable. Sometimes we have periods of drought and sometimes periods of prolonged rain. April is very showery and occasionally we have snow in Winter.
However, when I turn on the shower, the water always comes out at the same steady rate.
This is because it has been stored in a reservoir and is released as required.

It is the same with the reservoir capacitor.
The capacitor is charged up by the pulses.
It stores the pulses of voltage and the load is able to use this stored power as if it were a steady supply available from a battery.
 

Looking at the first waveform, the red line indicates the voltage across the capacitor.
When the first pulse arrives the capacitor charges up to the peak voltage.
When this pulse has ended, the capacitor voltage starts to fall as the load takes energy from the capacitor.
However, the voltage falls only slightly before the next pulse arrives to recharge the capacitor to the peak voltage.
The result is a DC voltage with a superimposed 50 Hz (in the UK) ripple.
This is shown in the second waveform.

At low frequencies the capacitor is usually an electrolytic type, but at higher frequencies, where smaller values are required, other types can be used.