How to select capacitor for the rectifier circuit

In order to how much cap to use where, you need to know a fair bit about capacitors in general:

• The different types (electrolytic, film, ceramic, tantalum, OS-CON, metalized film, etc.)
• Their characteristics (impedance, ESR, ESL, polarity, temperature rise, dielectric, etc.)
• Their failure modes (aging, over voltage, reverse voltage, thermal runaway, etc.)

You also really need to know why a cap is being used for a particular purpose, such as:

• Power supply output caps: less to do with holding the voltage up, more to do with ensuring the ripple voltage isn't excessive
• Power supply input bulk capacitors: mainly to do with hold-up time (keeping the output up for a short time after the input is removed)
• EMI filter: providing specific frequency attenuation, in coordination with other filter components
• Decoupling: providing instantaneous current to a circuit; a function of the circuit and the physical layout

Good luck with your knowledge quest. It will take some time but as you gain experience, things will get clearer.

I assume you're talking about C5. This capacitor makes sure that the voltage input of the 7812 is a smooth one. It works like this:

Image Reference: http://www.electronics-tutorials.ws/diode/diode_6.html

The heavier the load (higher current), the faster the capacitor discharges, thus the more ripple there will be. We want an input voltage (to the load) as smooth as possible because sometimes a device acts weird due to a power supply with too large of a ripple.

When the load is so heavy that the ripple is too large, you can use a bigger capacitor, because that smooths the line more. Therefore, it depends on the load what value you need for a capacitor.

You can calculate the capacitance needed for the capacitor for a given mains frequency (not so important) and load current - however, I'd prefer testing around a bit and measure the ripples with a scope.