After almost ten years of dedicated study of Epicurean philosophy, the best summary of the most important points I can produce is:
1 - There are no supernatural gods.
2 - There is no life after death.
3 - Pleasure is the Guide of Life.
4 - Happiness Is the Goal of Life.
5 - Truth is found through the sensations, anticipations, and feelings, rather than through logic.
Let me explain my reasoning:
The first two so directly follow from PD1 and PD2 that I see little room for debate - they are the obvious conclusions.
Some will probably argue that 3 and 4 are not so obvious, but I do think they are the logical extensions of PD3 and PD4. The distinction between "Guide" and "Goal" needs the most reflection. Lucretius specifically uses the phrase "divine pleasure guide of life" in his poem, so we have that textual basis for asserting that pleasure is best thought of as a faculty that serves as our constant guide while living. The letter to Menoeceus addresses both "pleasure" and "happiness," and it appears that the Epicureans did speak in terms of pleasure as being a "goal." Surely that means that they considered the clear meaning of happiness to be the predominance of pleasure over pain, so using pleasure and happiness interchangeably in many contexts makes sense. But the important distinction is that it is clear that Epicurus taught that we do not ALWAYS choose pleasure, when avoiding pleasure or choosing pain for the moment will lead to longer-lasting / more intense pleasure over time. We can legitimately say that choosing pain in the short run for the sake of choosing pleasure in the long run is still choosing pleasure, but it probably makes sense to assign the concept of "long-term pleasure" to another word - with that word being "happiness."
Also, I think that 3 and 4 as written here track what is considered to be PD3 and PD4. (Note: As I understand it, the division of the doctrines into 40 chunks cannot be traced to Epicurus himself, or even to as late as Cicero's time. It appears to be an overlay added for convenience some time well after the founding Epicurean period.)
PD3 states that the limit of pleasure is reached when all bodily and mental pain is removed. That is a philosophical argument aimed at the Platonic claim that pleasure cannot be the guide of life because it has no limit, and that anything that has no natural limit must itself be tempered and guided by some separate and outside force, which they assert to be "reason." So in other words, PD3 is the philosophic key to understanding that Pleasure is the Guide of Life.
PD4 states that bodily pain, which we fear most, is short when intense and manageable when of long duration, with manageable stated to mean "allowing an excess of pleasure over pain." What is this but a statement that "happiness" consists in a life in which we should pursue pleasure, and accept the pain that is necessary to achieve that pleasure, and that the resulting net of pleasure over pain over time is desirable: and is this not what "happiness" is all about at the last level of analysis? Considered in this way, "happiness", defined as the long-term predominance of pleasure over pain over time, can be seen as the goal of life.
Item 5 of this list is the most difficult to summarize in a few words, but this formulation I think addresses the most important point that we know from the Principle Doctrines and from Lucretius about Epicurean Canonics - that logic is at best a secondary aid to the sensations, anticipations, and feelings. A thing is what it is to us because of the way it is perceived by our sensations, our anticipations, and our feelings - not because our minds assign a word/concept to it as if it then partakes in some kind of mystical logos/logic.
I think it is useful to compare the first four of these to the "tetrapharmakon" found in the Herculaneum papyri. I have always considered that list to be murky at best, not the least because we do not have the full context to know what was being discussed before and after these few lines in the text. No doubt they were intended as a commentary on the first four doctrines, or at least as a memory device, but for all we know the text that was lost contained criticism of them or limits to their use. The form in which we have them is generally translated:
Don't fear the gods.
Don't fear death.
Whats good is easy to get.
What's bad is easy to avoid.
Without the textual commentary that is now lost, it remains my view that these are very easy - too easy - for the modern mind to misinterpret. Yes they are literally true under the Epicurean viewpoint, but so much of that viewpoint is unfamiliar that the new reader is regularly confused.
"Don't fear the gods" leaves open to the modern mind that Supernatural Gods may exist. That viewpoint is prohibited in Epicurean philosophy, which repeatedly states that there are no supernatural gods.
"Don't fear death" leaves open to the modern mind that death is not to be feared because we all go forward to eternal bliss in heaven. That viewpoint too is prohibited in Epicurean philosophy by the clear and full text of PD2.
"What's good is easy to get" leaves open to the modern mind that the best life comes automatically by simplifying living standards to the bare minimum. That viewpoint too is prohibited in Epicurean philosophy - see VS 63.
"What's bad is easy to avoid" leaves open to the modern mind that pain is a concern to be lightly dismissed. That viewpoint too is prohibited by Epicurean philosophy - the entire course of study is aimed at pointing the way toward pleasure and away from pain, and no one asserts that the study of nature comes without effort.
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I think it's good to go over and over these issues in one's mind, as that is the best way of understanding them more clearly and seeing their implications.