Credibility of Vedas and Puranas
Note: the Puranas are ancient histories found in the Vedas. According to Bhagavad-gita, verse 10.18, "The Puranas are histories of bygone ages that relate the pastimes of the various incarnations of the Lord."
In general, people find it difficult to place faith in something they perceive as "super normal" and/or beyond their senses. But many of the things they do place their faith in are quite unworthy of faith. For example, various Darwinian theories on the origin of life have now been found to be highly questionable. At one time people thought the earth to be flat. Many ideas about health have been proven wrong. Conversely, many people are realizing that ideas, originally found in the Vedas, about yoga and cow dung, for example, are actually correct, although at first they were considered "weird" or impossible.
How can they accept that the world was created by a "big bang?" Where's the evidence? Have they ever seen any thing happen in that manner? Maybe they can explode their next house into existence ;-). How do they know what they read on the Internet isn't just the ranting of some madman? (it often is, yet they search there for "truth").
Furthermore, it's very easy to understand that our senses are imperfect. What we see isn't always correct. Stars appear tiny to our eyes, yet they're huge. The sun also appears quite small, yet it too is enormous. If it's dark, I can't see my hand in front of my face, and many can't see well at all without corrective lenses. There are sounds that we can't hear, yet animals can hear them and radios can pick them up. We can't see wind or electricity, but we know it's there by its symptoms.
At least with these understandings one can realize that the ability of the human to KNOW what is reality, what is "true," is very limited. Thus we find ourselves putting our faith in politicians and scientists who have, repeatedly, fed us lies and led us in the wrong direction due to greed, envy, and other ill motivations.
On the more positive side, anyone who's open-minded enough to take up chanting, associating with devotees, eating prasadam and reading Srila Prabhupada's books they will often begin to understand and experience the potency of the Hare Krishna philosophy and the Hare Krishna Mantra. As they experience these things, their faith will grow and they'll find it easier to accept various parts of the shastra (scriptures).
To try to convince people of these esoteric things prematurely may be a mistake. One must learn to walk before running. So better to help them to keep an open mind and then begin to explore the more tangible aspects of Krishna consciousness...until they can become purified enough to accept the Vedic literatures as axiomatic truth.
After all, they accept the news and the newspapers, so why not just accept that Krishna is God and try to chant His name and eat some prasad...and suspend judgment for some time. Gradually everything will become clear.