You need to understand that their experience is highly emotionally significant for them. Not necessarily in a good way, but it is. For affected people it feels true - it "is true". What medications tend to do - they dampen the affective significance, among other things, and people in time become more able to be in touch with ordinary reality. By definition delusions are "unshakeable beliefs".
Having said that - it is known that there are possibilities of treatment without medications, or at least minimising their use. They tend to involve group and community based psychological interventions over long time. Scandinavian countries (e.g. Norway) do a lot of work in that regard. From my colleagues I have also heard that medication use is less in India - but the family ties and family member availability seem greater hence it becomes more of a group intervention. The model is that many family members in a loving way provide information that conflicts with the delusional content.
Then there is http://www.isps.org/ - a reputable organisation for psychological and social approaches to psychosis.
I hope this shows you to not expect a solution that you might be able to effect on your own. The psychotic experience can be very disturbing and you may be in for something that you do not expect when trying "to talk this person out of their delusions". Often you can become a part of the delusion - which then lessens credibility of what you say in the person's eyes.
P.S. Of course - we can have a different picture in illicit drug induced psychosis - by definition psychosis should abate soon after drugs are out of the system. It happens however that with recurrent drug use people develop psychosis that does not abate.