They are commonly either large aluminum cylinders mounted to the top of the chassis or large cardboard cylinders under the chassis with several colored leads. Usually there are two (2) or more of them. They can be one (1) part, two (2) parts or sometimes three (3) parts.  Each part can have a different voltage and value. These capacitors are used for power filtering.
They are VERY prone to failure and must ALWAYS be replaced.   One of the golden rules in antique restoration is NEVER, EVER plug a radio in without checking the electrolytic capacitors, they may very well be shorted and can burn up the power transformer.
Electrolytic capacitors are usually the reason for a loud hum or buzzing, but are not always the problem.  If you find one that is bulging or has exploded, suspect that it is wired incorrectly.  If they are mounted on top of the chassis and are the can type, check to see if they are mounted in a cardboard cylinder or if there is a fiber washer between the can and the chassis.  If there is a washer or cardboard cylinder, they are not grounded to the chassis.
Take a look at the blue and black capacitor at the top of the page. Notice the arrow on the side of it.  The arrow is pointing to the NEGATIVE end of the capacitor.  If it has wires the NEGATIVE wire is black.  Notice I did not say ground!!  Itís NEGATIVE.  Electrolytic capacitors ARE polarity sensitive!  You must have them wired positive to positive and negative to negative.  Now they MAY have negative to chassis ground, and they MAY not.  If you donít know which way they go, FIND out, DONíT guess.  Check the schematic and if you canít figure it out, ask someone.
As far as replacing the electrolytic capacitors, you have many options.  Some top chassis aluminum cylinders are available but are very expensive and hard to find.  Usually it is much easier to just install axial lead caps under the chassis.  There is usually lots of room after the paper caps have been replaced.  It is best to avoid using the original can terminals for connecting the new caps.  Disconnect the wires from the old cans and leave it mounted to the chassis for appearances sake.  The electrolytic sections could short and render your restoration useless.
Remember to use new caps with a voltage rating equal or greater to the original voltage.  When in doubt use quality units of 350V or 450V.
Below are some examples:
39-25 PHILCO schematic lists     2 of 16 mfd  250V  USE 2- 22mfd  450V
38-12 PHILCO schematic lists      
1 of   8 mfd 400V  USE 1- 10mfd  450V
1 of   4 mfd 250V  USE 1- 10mfd  450V      
1 of 12 mfd 400V  USE 1- 22mfd  450V
 60 PHILCO    schematic lists        
2 of   8 mfd 250V  USE 2- 10mfd  450V
37-620 PHILCO schematic lists    
1 of   8 mfd 250V   USE 1- 10mfd  450V
1 of 12 mfd 400V  USE 1- 22mfd  450V
1 of 16 mfd 400V USE 1- 22mfd 450V
40-180 PHILCO schematic lists    
1 of 12 mfd 400V  USE 1- 22mfd 450V
1 of 16 mfd 400V  USE 1- 22mfd 450V
A power supply filter can be replaced with one as much as 50% over the value, but keep in mind much higher could result in increased transformer and rectifier surge current when powering the set up