I'd ask your motivations for wanting the person to understand their delusion... if it's for their safety, then you do what you can to facilitate their safety (if appropriate) or refer to a psychiatric clinician for possible inpatient admission until they are safe...

If it is for your mental well-being, my cold-hard advice is to just learn to cope. Some delusions are fixed and do not, ever, go away. By definition, delusions are an inability to perceive things as they are in that moment... so it's a lost cause...

Best case scenario is that this individual can realize that they have a tendency toward delusional thinking... you could work on helping them develop skills that recognize reality from delusion. One of my faves is having people ask questions any time they doubt their own sensations... "did little bobby really poison my food or is it possible my brain is just overreacting a little tonight?"

approaching them with the "why can't you see" attitude won't work... b/c they can't see.

if it is damaging to you, however, don't listen... i know that's what Chris said to avoid... but truthfully, you can't go down for someone else, anyone else... so if this person's delusions are abusive toward you and you are unable to remain in the relationship, then refer the individual for care and try to heal from your experience... then, move on with your life...

you do not have to fix anyone nor should you feel obligated to remain in a position of service to someone who is pushing you to an unsafe distance...

another option is to just ignore it... if the delusions are not life threatening, why do they have to be realized? if someone wants to believe in purple unicorns in their bathtub... and those unicorns aren't hurting anyone... then, i'm going to let them believe that purple unicorns live in their bathroom...

everyone has their own perception of reality... it just so happens that we label some people's perceptions as wrong or symptoms...

good luck with this individual, i'm sure it's very frustrating