DR is one of the facets of the game which could use a thorough thread somewhere but if there is one i have not found it.
What I know I have learned from experience and conversations with other players some of whom believe myths that are obviously not true.

I will take an initial stab and hopefully any errors will be corrected by admins and players who actually know. I predict there will be some additions that are just flat wrong.

DR stands for diminishing returns. DR occurs any time a country has been attacked more than once in any 24 hour period. The yield from the attack is lowered because the target country has been hit within 24 hours. The yield from each subsequent attack within the 24 hour period is diminshed by ever larger amounts. That is why you will frequently see five LGs on a country in Express in a 24 hour period and no more than that because after five the yield is substantially reduced. I have looked for the %s but not been able to find them. I have asked a couple of clan leaders who did not know the %s and you will note that the first responder did not address that specific question.

Assume your country has not been hit in the last 24 hours
your DR is 0 after you are hit it is 1
any LG on you at 0 will result in an undiminished return
any subsequent attack within the 24 hour window is diminished by degrees as the number of LGs rises
if your DR is 3 the attacker receives less than if your DR was 2
e.g. a player hits you the first time he receives 200 acres
a second hit results in 186 acres which is 200- DR

sometimes you may see that the second hit or even the third hit actually acquires more land than the original hit. This occurs when other factors override the small amount of DR. This is especially true when you are hitting a higher NW country. EE gives the highest % yields to LGs in close proximity to your own NW. So as your NW gets closer to your target your total yield rises despite the DR factor.

Boxcar and some of the other clan sites have DR calculators but on express you can do it yourself simply by checking the news to see how many times your target country has been hit in the last 24 hours.

So let us look at a couple of examples and conclude:
a) you see in the news your target country has been hit three times but all the hits are over 24 hours old, your first hit is undiminished
your second hit is essentially undiminshed
your fifth is greatly diminished

b) you see that your target has been hit in the last 24 hours and your predecessor got 360A, your yield will be slightly diminshed and will be more influenced by factors such as relative size and gov types than by DR

c) you see in the news your target has suffered one SS, 2 NMs, 2 EMs and three ABs. You see that after these attacks your target launched a PS and acquired 1000 acres of land.
What is his DR?
Many people will tell you that his DR is 0 becasue he launched an attack. That has not been my experience. Slagpit recently stated that the admins are considering making the rule in Express that DR evaporates immediately once a country launches an LG so that means the current rule is that subsequent attacks do not eliminate DR but from my experience do lower your DR.
Anyone who has hit an AB victim within 24 hours knows that DR is still in place in fact sometimes your attack bounces.
Qzjul recently stated that EMs do not effect DR on EE, he further stated he did not believe they ever did. Again that has not been my experience on swirve or mars2025.
i once had an ally at earth2025 who gsed me five times a day in the belief that this would increase my DR. When push came to shove, i got crushed so evidently on Earth2025 GS DR was substantially less than LG DR and that appears to be true on EE as well. Do not hit someone who has been gsed 34 times twelve minutes ago. I do not know how much each missile strike effects DR if at all or the %s of DR produced by the special attack types.

if someone could explain exactly what the DR in example c) is and how any new rules impact that DR, i would appreciate it.