See Bostrom's simulation argument for background. From a practical standpoint, you might be suspicious that you live in a simulation if you inhabit a world with the following characteristics:
Hint #1) Limited resolution. A simulation would be computation intensive. It would be useful to have tricks that increase the economy of operations, but in ways that do no compromise the consistency of the simulation to the players. One such trick would be to set an absolute upper limit to resolution (or a lower limit to the size of the elements that make up the "picture") that is below the sensory threshold of the players. These elements could variously be called pixels or quarks. Similarly, it would behoove the simulators to set a maximum time resolution, i.e. maximum frames-per-second, also called Planck times. Furthermore, the simulation's computing power is spared by a statistical method of calculating relationships between entities in the simulation (i.e quantum mechanics) even though it may look, at the scale of the game players or simulated entities, as if the universe maintained quantitative relationships in terms of integers calculated to arbitrary precision. (Related question: is it possible in principle given the physics of our universe for something the size of a bacterium or virus to "be conscious of" this gap in the behavior of the Newtonian and quantum realms, at a very basic sensory level? If not, isn't it interesting that our universe is such that there can be no consciousness operating on scales that would expose the twitching gears behind the scenes?)
Hint #2) There are limitations in what spaces within the game can be occupied by players or sims. In the old Atari 2600 Pole Position game, you couldn't just randomly go off driving off the track and through the crowd even if you didn't care about losing points; the game just wouldn't let you. Similarly, the total space in our apparent universe that we occupy, or directly interact with, or for that matter even get any significant amount of information from, is an infinitesimally small part of the whole. Unless you're in a submarine or in orbit, you don't go more than 200 meters below sea level or 13,000 m above it. (That's a volume of 2.1 x 10^18 m^3 that for all practical purposes the entirety of human history has occurred in; double that figure, and that's the volume that all of evolutionary history has occurred in.)
Hint #3) Beyond the "active game volume" as described above, dab a few pixels here and there in an otherwise almost entirely dark and empty volume. Make them so far away that sims can't possibly interact with them. Reveal additional detail as necessary whenever someone happens to look more closely at them. (And there's another trick: objects in this simulation are only loosely
defined until one of the players interacts with them, "collapsing the wave function". Yeah, that's what the programmers will call it, that's the ticket.)
Hint #4) Even in that limited location, make the active game volume wrap around. That way the simulators get rid of edge-distortion problems, as in Conway's Life. A sphere is the best way to do this. Therefore, work out the physics rules of the simulation to favor spheres.
Hint #5) Make each state of the simulation dependent on previous states of the simulation, but simplify by dramatically limiting the number of inputs with any causal weight. The simulators can limiting computations by having only mass, charge, space and their change over time determine subsequent frames.
Hint #6) If for some reason it is important for the entities in the simulation to remain ignorant to their existence as part of a simulation, the simulators could make sure the entities are accustomed to not only these kinds of stark informational discontinuities but to profound differences in the quality of awareness, both within themselves and each other. That is, the sims will accept not just that the vast majority of the universe (as seen in the sky at night) is interactively off-limits to them, but they'll also accept that their own awareness thereof and ability to connect the dots will dramatically vary over time. That way, if there is any need to interfere and make adjustments (to stop someone from figuring out the game) it won't strike the sims as strange. (Forgetfulness, deja vu, mental illness, drugs, varying intelligence or ability to concentrate on math, death of player-characters before they can learn too much?)
#6 does raise a very important question: why would the simulators give a damn if we knew we were in a simulation. So what? What would we do about it, sue them? If Pac-Man woke up and deduced that he were a video game character, if he still experienced suffering and mortality the same way, why would it matter? By this same view, there's an easy answer to whether we should behave differently if we're actually in a simulation: no. Whether our universe is in reality just World of Warcraft from the sixth dimension, if we simulated beings can suffer (and I know I can), then the moral rules are exactly the same as before.
It's also worth asking for some humility, and asking why we humans always assume that we would be the purpose of any such simulation. We could be merely incidental consciousnesses that are necessary for harboring the populations of simulated bacteria that the simulators are really studying. Or, the simulators could be cryonicists who preserve pets, and the most popular pets in their dimension look like what we call raccoons, and our universe is actually the raccoon heaven in which their beloved masked companions await a cure for the disease that forced the owners to put them on ice. In fact the raccoon-heaven simulation would contain a whole suite of ecosystem, all of them purely simulated (with the exception of raccoons) to keep up the appearance of a full biosphere. So the point of such a simulation would be to fool raccoons - or maybe even mice (again, why would they care about fooling everyone! If the simulators are reading this, just give me more juicy steaks and I won't make problems. It doesn't cost you anything!)
While the raccoon thought experiment is meant to be whimsical, a healthy respect for our own ignorance is always in order for these kinds of speculations. After all, assuming what we have guessed about the rest of (for the sake of argument simulated) universe is accurate, then there might be "aliens" (other non-human intelligences within the simulation) who may very well be much brighter than us. So even if the simulation is somehow arranged around the most intelligent entities within it (as we assume), those entities need not be human. Even if we're simulated, and we have a real brain and body in the "real" universe that's similar to our form in this one, this simulated universe might be designed for Martians (who are brighter than us) and be much less pleasant than our home dimension.
Finally, the very idea of a simulation is poorly defined. Mostly we think of something like almost completely controlled full-world simulation in the Matrix, but let's explore boundary cases. If I wear rose-colored glasses, is that a simulation (or a red world)? What about LSD that causes me to see unidentified animals scurrying past in my peripheral vision? What about DMT that causes a complete dissociation of external stimuli from subjective experience? What if I have some chip implanted that displays blueprints of machinery in my visual field a la the Terminator, is that a simulation? What about a chip that makes me see a tiger following me around that isn't there? (Hypothetical given current limitations.) What if I hear voices telling me to do things that are produced by tissue inside my own skull, by no conscious intent of anyone? (Not at all hypothetical.)
One of the interesting points in the popular movie Inception is the way that external stimuli appear in dreams. This gives us a hint as to what we mean by simulation, and why we care. Most of us have had experiences where the outside world "intruded" into a dream, with the stimulus obvious after we awoke. I once dreamed that a dimensional portal slid open in front of me with an ominous metallic resonance, and I stepped through it, suddenly speeding over the red, rocky surface of Mars. Then I realized it was my father opening his metal closet door in the next room, and I was looking into that room at the red-orange carpeting. Before I was fully awake I had received the sound stimulus but I had built a world out of it that most of us would not regard as real. (The experience of speeding over Mars was quite real, even if most humans would have a more accurate representation of that auditory stimulus.) So, a better way of saying "how do I know 'this' is reality, rather than another dream, or a simulation?" is to ask "how do I know I am perceiving "true" stimuli, without mapping them unnecessarily onto internal stimuli, giving me as accurate and un-contorted a view of the world as possible?"
And indeed in certain ways, we certainly are dreaming, in the sense of injecting internal stimuli and filtering external stimuli through them. (Notably, it is possible to view schizophrenics as people who experience dreams even while awake and filter their perceptions accordingly.) First and most obviously, because our sense organs are limited in what they can detect, we're obtaining only a slice of possible data. Second, the world we knit together is the result of binding of sensory attributes into object/events, as well as pattern recognition. The limitations of our nervous systems, and the associations we are able to make, profoundly influence the representation we build of the world we're perceiving.
Third, and most significantly, a large part of our experience is non-representational: emotions, pleasure and pain do not exist outside of nervous systems, or rather the events to which those experiences correspond are almost entirely contained within nervous systems. Yes, to be precise the experience of light does not exist until the triggering of a cascade of electrochemical events by radiation incident on pigments in retinal cells; but light, which is what is represented in our experience, exists traveling across the universe. Pain and happiness do not. These are internal stimuli that add a non-representational layer to reality, even more certainly than my dream of the Mars overflight.
A good working definition of a simulation as it is commonly understood is when the majority of one's external stimuli are supplied deliberately by another intelligence to produce experiences that do not correlate to physical reality external to the nervous system (or computational equivalent). This avoids taking a position on AI; the sims may or may not be entities separate from the computation. I.e., you might be in sensory deprivation tank like Neo, or you might be a computer program. The question of reality versus dreams or simulations is not one of discrete "levels" as we've come to think of it in popular culture. It is rather a question about how we know our experiences correspond in some consistent way with events separate from our nervous systems.