Dreaming, the ability to have prophetic dreams and the related Talent of Dreamwalking, the ability to intentionally enter Tel'aran'rhiod (TDR, Ch. 21) while asleep are not of the One Power, though Aes Sedai believe they are (TSR, Ch. 23). It is not clear if a person who has one ability will naturally have the other, though the four Aiel Dreamwalkers, Egwene and Perrin can all do both. However, even when Egwene knew she was a Dreamwalker, neither she nor the Wise Ones knew for sure if she would also be a Dreamer (LoC, Ch. 15). For the Aes Sedai at least, the two are interchangeable and the term “Dreaming” is used for both abilities (TDR, Ch. 21).
Dreaming, or having prophetic dreams, is linked to tel'aran'rhiod. Aes Sedai believe it linked to foretelling (TDR, Ch. 26), though as it is not related to the One Power, they are most likely simply mistaken (TSR, Ch. 23). Unlike Foretelling, the dreams do not tell of what will be, only of what might be (TSR, Ch. 23), but a Dreamer’s dreams about ta’veren were almost always significant, and the more strongly ta’veren, the more likely (TDR, Ch. 25).
The Dreamwalkers in the book often have prophetic dreams
Dreamwalking, the ability to enter tel'aran'rhiod is a rare ability, found among both those who can channel and those who can't. In all of the Aiel, there were only four, two of whom could channel and two who could not, though as there is not necessarily a way of identifying Dreamers, there may have been others undiscovered in the general population (TSR, Ch. 23). In general, those who are not dreamwalkers require ter'angreal to enter, though Aviendha implied that she can enter the dream with the help of a Dreamwalker. Birgitte stated that a person who knows they are in the World of Dreams can be found from that, as there is a feel to them (TFoH, Ch. 14).
As tel'aran'rhiod can be dangerous, dreamwalkers will destroy any nightmares they encounter, which can otherwise take on something of a life of their own, and a person who has unwittingly stepped into tel'aran'rhiod can be drawn in, unable to escape.
One of the advantages of visiting tel'aran'rhiod is to find something using need, a person focuses on thinking about what they need, or a problem they need a solution to, and they can be taken to the solution (LoC, Ch. 13), though if they don't take careful note of where they are, they can't find it again (LoC, Ch. 52)
Other people's Dreams
Dreamwalkers also have ability over other people's dreams, in several ways, firstly, finding and appearing in them, which is much harder than stepping into Tel'aran'rhiod, especially if the person is far, or not known well (TFoH, Ch. 5). Entering the person's dream is always a risk, as it takes all your effort to remain yourself and not what they make of you (TFoH, Ch. 5). Simply watching is much simpler (LoC, Ch. 14), and the Wise Ones use this to spy on Rand (TFoH, Ch. 49). Unless a Dreamwalker seeks out the dream and deliberately looks into it, they will not go into one, unless there is love or hate that is very strong (LoC, Ch. 15). This is not something that can be taught.
Secondly, they can bring them into the world of dreams. The Wise Ones consider this an evil thing, something the Shadow used during the War of the Power (TSR, Ch. 52). Temaile did this to Amathera (TSR, Ch. 54). People may touch the World of Dreams accidentally, but would generally not realise it was anything other than a vivid dream (LoC, Ch. 14)
Aes Sedai and Tel'aran'rhiod
Aes Sedai have long since lost all but a very basic knowledge of Tel'aran'rhiod and Dreaming, the most recent Dreamer was Corainin Nedeal, four hundred and seventy three years ago (TDR, Ch. 21), though Moiraine thought that there hadn't been one in almost a thousand (TGH, Ch. 42). They believe it linked to Fortelling (TDR, Ch. 12) and the One Power (TSR, Ch. 23), a thing of spirit (TDR, Ch. 53). Moiraine also believed that she could have tried Dreamwalking (TGH, Ch. 42). The White Tower possesses a number of ter'angreal that allow entry into the world of Dreams, but most have not been studied since Corainin was alive (TDR, Ch. 25), including several that were originally used to train students (LoC, Ch. 7).