When an airliner gets lost, and receives warning shots from interceptors, how should the pilots react in order to save the aircraft? In 1983 KAL007 was shot down by the Soviets, as it got lost due to navigational errors and entered restricted airspace. The Soviet interceptors reportedly fired warning shots "which were likely not seen by the KAL pilots", and after then they proceeded to destroy the airliner with an air to air missile.

So, let's suppose you are flying a commercial flight, when a military aircraft catches up to you. If your communication equipment wasn't malfunctioning, you would have already gotten demands to change course and you could have identified yourself, answered that you will comply, and could more easily avert the problem. For this case, let's suppose your comms are down due to technical problems.

You then see you are fired upon (how? smoke trails of a missile flying by? Tracers from guns whizzing past?). It is only then when you realize you got intercepted, and you suddenly realize they just fired warning shots at you. 

What now? How could you maximize your chances of survival? I would guess you have to indicate surrender, that you will comply to any instructions, and that you mean no ill will. How can you do that without a working radio? If you just entered a country's territory, the most obvious way would be to change course to the shortest path leading out of that territory, but if you are deep inside, or you are lost, you might choose the wrong heading and make the problem even worse.

Is there a custom how a civilian aircraft can indicate "I yield, please don't shoot me, I will follow your orders!"? And, lastly, how would it differ between the incident happening in 1983 versus 2019?
First off there are established interception procedures under international law so they are not going to shoot at you upon overtaking you.  Typically an element of fighters form up on the jet with the leader maneuvering into formation on the jets 9 O’Clock and the Wingman stays on the jet’s six.  They will do so in a manner which allows the intercepted aircraft to see the lead fighter.  There are a series of established visual signals ie rocking wings for compliance, deploying flaps and landing gear, etc.  if the intercepted aircraft cannot communicate with the fighters or ATC, they will squak 7600 and ATC can relay this to the fighters.  Other means can be employed to get the attention of the intercepted aircraft such as the lead fighter cutting in front of the intercepted aircraft while in afterburner, etc.

If it does come down to where the authorities determine you are a threat and use of deadly force becomes authorized, the fighters are going to let you know in a clear and unmistakable way.  Unless you are armed and intend to engage, you better comply!