What is the correct approach for a skeptic to take when there is insufficient evidence of a claim, or it is not possible to reproduce or validate a claim made?

To better illustrate my point, I will use the man on the moon claim.

I believe that men have been to the moon because it is reasonable, because it is simpler than the conspiracy theories and because the arguments against that claim are easily debunked IMO.

However there are people who are skeptical of that claim, and given that we can't reproduce the result again (or most people can't due to a lack of means) then is it right to be skeptical?

In short where do you draw the line between needing to see something to believe it or basing a conclusion on reason and logic and the evidence available?