Past, present, future, dreams, memories, etc. These are all concepts we've created in an attempt to explain the present moment. Memory refers to one aspect of Now that we're trying to make sense of. Time is change. Finding the minimum possible change that must take place between two instance will give an indication of what we call duration. There is only one minimum distance, because of the principle of least action. The math is simple for showing everything about a system of three bodies, but becomes impossibly complex as more are added up to the number of individual particles in this universe. However, the fact still remains that "duration" is the measure of the total difference between two complete instants.
Because every instant is possible (and exists in some sense), all our memories are merely records of other instants. Often they contain enough information that relates to differences from the present moment that we can make some sense of duration. In addition to memories, one might say, there are also external records, but in order for an individual to really have access to these, they have to be already contained within that person's mind (i.e. memories of reading about it or whatever). Therefore, let us only concern ourselves with the records contained in memories.
The "past" is really just the collection of all instants for which there are memories in the present. What separates the "real" past from "false" memories and dreams is only the existence of similar memories in other people, along with perceived records in the "external" environment. If such parallel records exist, then it "really" happened. If they don't, then it is usually described as a dream or as false memories created in a dream. One may claim that this simplistic explanation leaves out the entire past "prior" to a person's earliest memories. However, we still possess records of the earlier past in memories, they're just memories of books or conversations or whatever.
What typically separates (in our own minds) "memories" from "dreams" is the idea of duration. That is, we have things in what we call memories that can be compared with things now, so some kind of duration can place it in time, or, even if it can't be placed in time (because of, say, a lack of observable differences between the memory and the present), it can usually be placed in space. Then the memory can be analyzed with physical evidence at that location to determine whether it is a real memory or a false one.
Even if such evidence fails to place the memory within this lifetime, past lives can be used to explain the record, provided that what evidence is available places the memory at an earlier time. (Some memories, which cannot be properly "verified" can still be explained via past lives, assuming that the person doesn't remember seeing any people from this lifetime there) Of course, past lives are no more arbitrary an explanation for such records as a linear progression of events in this life. The main reason past lives aren't as accepted in the West is that most people lack such memories. As I explained above, when too few people share similar records, it is deemed to be a "false" experience, even though it is obviously real to the person who has it.
In what we call "dreams," on the other hand, some characteristics place the records outside the realm of "waking reality" even in the mind of the person who has the dream. These characteristics are typically related to a lack of consistency within the dream. We all remember dreams in which everything suddenly changes drastically, such as the surroundings or characters. While this is not surprising within the context of the dream (because the changes are usually brought on by our own thoughts, so we know they're going to happen ahead of time), upon waking, we remember the strangeness of it all and call it a dream.
Of course, there's also the fact that memories we perceive as coming from the area between going to bed and getting up are called dreams. We do this simply because "external" records don't exist supporting the idea that whatever happened in the dream "actually" happened. We don't notice this process much as adults, because we've simply gotten so used to dismissing memories of sleeping as being mere dreams, but we do constantly evaluate all the records we have, categorizing them as memories or dreams.
The concept of "present" is the label we give to the precise instant we are currently observing. However, while what we are actually observing is within a fairly small volume of space (entirely within our own brains, if you assume the actual act of observing something occurs only once the signal has reached the brain), our ideas of the present extend far beyond our own bodies. This is because memories we see as being more recent memories (due to smaller perceived duration between them and the present) are combined with current observations to form our entire idea of the present. Even though we may no longer be observing whatever was in the memory, we assume that it is "still" going on in this instant.
Future, in a nutshell, is the collection of all instants containing the same basic records of the present (i.e. sharing the same distant past) along with some kind of record of this instant itself. Many of these future moments are extremely bizarre, though, since in every large-scale configuration of the universe, it is possible that a copy of one's mind exists along with memories placing this moment in it's "past."
Therefore, more criteria have to be looked at if we are to talk about more "likely" futures. We do this again through memories. More accurately, we look at the "past" that we've already arranged to accommodate all the memories. This "past" has all the memories laid out on a timeline with distance between them representing duration. Though this past is only an interpretation of present records, we can only have a useful idea of the future if we assume, at least unconsciously, that such a linear progression between moments does actually exist.
Once the existence of a coherent past has been assumed, we can look for, and invariably find, patterns in our memories that correspond to perceived trends in what we call the past. What we usually think of as our possible future is only the tiny fraction of all futures (as defined originally) in which the records create a past in which these same trends have continued, more or less.
Thus explained, it can be seen that all of our notions about time are merely explanations we've come up with, which are now deeply ingrained into our subconscious, to explain nothing more than our current mental state. What we usually call the external universe is actually entirely contained within our own minds. Sure, there is definitely something bigger than us that makes what we observe fit some kind of pattern on the larger scale of the universe (which is why we can formulate scientific laws that hold true time after time), but the fact remains that everything we have is within the present state of mind.
Apart from the fact that what we call reality is more consistent than what we call dreams and fantasies and simulations, there is no qualitative difference beyond this. Thus the only thing we can really do is be aware of our present state of mind in this moment, and all "future" moments, because everything we are and everything we can be is right here, right now, rather than somewhere "out there."