Dream magic is a rare trait, similar to metamorphmagic in the sense that it is a genetic ability rather than a learned one. More common in the Middle Ages, it has become something of a sport gene and is not easily bred for, but it does occasionally crop up, generally in bloodlines that have reinforced. The gene, being recessive, requires both parents to have it as a latent ability, but latency is no indicator of expression; unless it is reinforced, it remains inactive, and parents may not know that they carry it until their children develop oneiromantic ability.
The magic functions differently for each individual, but broad parametres may be drawn. The dream is entered at a place best referred to as "neutral", but it probably resides in the mind of the dreamer. Through whatever method of movement that presents itself, the dreamer may find the dreams of someone who is actively dreaming. It is rather easier to get to a random dream, but it is possible, with a great degree of focus and training, to learn to cast a mental hook to reach the person one wishes. If they are asleep and in a dreaming state, the hook can be followed to lead the oneiromant to their target.
Once in any dream, oneiromants have a choice of options - witnessing without disturbing or disturbing the dreamer and making them aware of the oneiromant. The dream as witnessed will be in whatever style the dreamer is accustomed to dreaming - without conscious effort, the oneiromant can't change what they see.
Interaction is possible, but the main point all oneiromants are made aware of is that any interaction in the dream may have consequences in the real world, though they are likely to not be as severe. A blow that leaves a bruise in the dream world may leave a faint mark in the real world.
Unless the oneiromant has gone with the intent of causing harm, the dreamer retains control of their own dream, leaving the oneiromant with the option of interact or retreat; neutral is always available to an oneiromant, but it also becomes available to a dreamer when a retreat makes the route to neutral visible.
In instances where the oneiromant is on a friendly, or at least neutral, visit to a dreamer, interaction of all kinds is quite possible. Conversation can be very amusing; most people, given the scarcity of oneiromants and the fact that people with that ability tend to be secretive about it, don't believe that what is really happening is, in fact, what is happening. The dream itself may also be played with and consciously altered, by both parties. If a dream of the slums of Paris is objectionable, why not go to the beach?
When harm is intended, all bets are off.
It is extraordinarily difficult to kill someone in a dream; blows that would kill in the real world will not in the dream world, because of the typical diminishing returns of offensive actions. The goal is to destroy the victim's coherent image of self enough to convince the body that it has suffered a shock strong enough to cause death. The results generally appear, on autopsy, to be that of dying of fright - the heart is degraded with adrenalin and may well be frangible, while other systems show shock trauma. The main discrepancy is the potential for marks indicating a fight, but to all other intents and purposes, the victim will appear to have died in their bed. Whatever the provocation the oneiromant uses, defensive wounds and postures are unlikely at best.
Alteration of the dream is also possible in a hostile meeting, but in this instance, the dreamer and the oneiromant are battling for control, and actions that are easy when the two are on positive terms become concomitantly more difficult.
The oneiromant must leave the dream before the dreamer wakes, dies, or forcibly ejects the oneiromant. In the first two cases, they run the risk of being trapped in the dreamer's dream, either forever or until that place is visited again (there is absolutely no interesting ability with that; an oneiromant separated from their body in this way tends to start physically decaying quite quickly, and given the nature of dreams, though the place the dreamer has arrived is likely a baseline dream (not the sort one consciously remembers) the dreamer may not return to it for several days. In the last case, the oneiromant risks being trapped between dream and neutral as the dream snaps off from neutral; again, there is very likely no return from that.
Falling asleep in a dream is both pointless and disquieting. The sleeper gains no refreshment from sleeping, and their dreams are merely a blank, vaguely opalescent wall of grey mist.