Given sufficient computational power and insanely sensitive measuring instruments, and assuming a sufficiently deterministic Universe, it may be physically possible to construct a machine enabling its users to observe the future to an arbitrary degree of accuracy, though it is extremely implausible that technology will ever reach a level in which such a set-up could be created. The view that would result from such a machine would be the future, even taking into account the effects this foreknowledge might have on the behaviors of anyone who used the device. This is probably the least fun version of prescience, since no one could do anything to avert any disasters predicted in this way.
A much more interesting version of prescience, which is common in science fiction (Minority Report, The Dead Zone, Next, to name a few), is that in which the future viewed is what would have happened, had the future not been viewed in this way. This leaves room for the foreseen events to be changed. Constructing a machine with this goal in mind would, if anything, be even more difficult than building the previous one, because it would have to be given a Universe configuration that differs from reality in a way that is not immediately clear. Would it be enough to remove from the calculation the particles that make up the machine? What about the particles that make up the brains of the machine's creators? How would the configuration be different had they not decided to build this machine, and how would such a change affect the rest of the Universe? To build such a machine, we would have to make assumptions about how to resolve these issues, but in so doing we would also lose confidence that the results are truly what we expect.
These previous models have one obvious failing, in that they ignore results of quantum mechanics; the Universe is not truly deterministic. A more robust version of the first kind of prescience might come from a sort of inverted causality, in which events occuring in the future affect the past, for example by giving knowledge of these events to some individual. This version also suffers from the logical implications of time travel, meaning that one cannot alter events foreseen in this way without reaching a logical contradiction. Assuming the Many Worlds Interpretation is correct, however, the forseen events could be altered, since presumably they represent only one part of the future Universe's wavefunction. Even this is problematic, however, because how can we say that the predicted events are what "would" have happened, if we've already admitted that they only represent one possible future?
Hence, it seems that we are left with two logical ways by which prescience could work. We could have a view of the actual future, which we are powerless to change. Or, we could have a view of a merely possible future, but without precise knowledge of what circumstances will lead to this future, leading to a tricky dilemma: will the actions I take trying avert the disaster I have foreseen actually be the cause of that disaster, in which case I should do nothing, or will inaction have the same effect? The best thing would be a combination of the two modes: the ability see the actual consequences of each possible action. This avoids the futility of the first mode; in this case you have an actual choice to make. It also avoids the uncertainty of the second mode; you can be sure that you know what the consequences of your actions will be.