I would second Sandy's advice that this is not an ideal project for a total beginner. Lots of capacitors to replace, many chances to make a wiring mistake. It would not be a bad idea to practice recapping on a cheap five-tube radio that you get at a thrift store or on eBay.
That said, this article gives basic information about capacitor replacement:
http://antiqueradio.org/recap.htm
Start with the electrolytic capacitors in the power supply. That reduces the risk that you'll fry something like a power transformer, which might cost more to replace than you paid for the whole radio.
A hum in the audio that doesn't change as you turn the volume control is the classic symptom of a bad electrolytic capacitor in the power supply.
Very cool boatanchor, by the way.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html