First of all capacitors is a term that was not always used.  The word condensers was used for a very long time and some place along the way it was changed to capacitors.  Most people call them "caps", so when you read that a radio has been "recaped", that means that the capacitors have been replaced.
The performance of the radio depends on the conditon of these "caps". Most often they will be badly deteriorated and they should ALL be replaced and NOT JUST the easy one's to get at.  They are cylinders filled with wax on the ends with a wire lead coming out of both ends.
Capacitors are found in all areas of the radio circuit for general coupling, decoupling and filtering.  They are NON-POLARITY sensitive and are usually clearly labeled with the value and voltage rating.  They often have a black band around one end.  This  end was connected to the less sensitive side of the circuit and for non-electrolytic ones it does NOT make any difference which end you connect.

Damage to the caps is usually indicated by melting, bubbling or darkening of the outer wax covering and loss of wax on one end.   Sometimes they look ok and test ok, but have electrical leakage and can act more like a resistor.
It is hotly debated whether or not you should replace them all as purists and collectors feel they should only be replaced if absolutely necessary.  Paper-wax capacitors are VERY prone to failure and it is just a matter of time before they fail, so I believe they should ALL be replaced.  Since the work is under the chassis and not visible, it should have little impact on the value.  People who look at my radios have never asked me to take the chassis out.
Before you expend a lot of effort trying to find the exact values, you come as close as you can to the values.  For example, a 0.05 cap you use a 0.047 cap,  for a 0.02 cap use a 0.022 cap and so on.  The voltage I use is 630 Volts on everything, that way you don't have to keep as many of them in stock.