If I'm designing a DC power supply, let's say 5V, how do I know how much filtering I need (capacitor) after the bridge rectifier (full-wave)? Is there something in the datasheet that would tell me? Is it advisable to just dump the rectified AC into the regulator without any filtering, or would I see some sort of half-square-half-saw wave coming out the other side?

 

for filtering in adaptor (after diode bridge) , big is beautiful, but be ware with the current drawn by the cap

 

No. We discussed this in another thread. The larger the capacitor, the lower the ripple voltage but the peak current in the rectifier diodes will increase. You really need to put some numbers into the design equations: what is your max load current, what is the target voltage, how much ripple to expect, what is the drop out voltage of the regulator. Remember that if your rectified voltage is too high and your regulator has to drop a lot of this, it is going to get very hot under full load.

In summary, get out your pencil, paper and calculator and do the math.