The main focus of skepticism about how long people lived in the Bible has focused mainly on the genealogies listed in the first several chapters of Genesis. Adam lived to be 930 years old (Genesis 5:5) and Methuselah, the oldest human, lived 969 years (verse 27). Noah, who was already 600 years old when the flood came, lived a total of 950 years.
What are we to make of all these advanced ages? Although undoubtably humans before the flood lived very long lives, those living after the deluge experienced lifespans that were significantly shorter. For example, Moses lived to the age of 120, which is slightly less than Jeanne Calment who in 1997 died at the age of 122 years.
The ancient Roman historian Varro asserted that to understand the REAL age of the patriarchs one must divide their lifespans by 12 (i.e., substitute lunar months for solar years). This, however, does not work when one considers the age at which the patriarchs sired their first son. For example, if we divide the age at which the Bible says Enoch had Methuselah (65 - see Genesis 5:21) by twelve, we end up having him become a father just after he turned five years old!
What might have caused the decline in lifespans to what we now accept as normal? There are ways to attempt to explain the difference in longevity although they are somewhat speculative. For example, Henry Morris and John C. Whitcomb in the seminal scientific creationist book "The Genesis Flood" promote the idea that because the earth's water was suspended above it (see Genesis 1:6 - 7; cf. 7:11) before the great Flood, it helped protect the patriarchs from ultraviolet radiation.
Such water in the atmosphere made for a better, more even and temperate climate throughout the earth. After climatic conditions radically changed after the Deluge, people on average lived shorter and shorter lives (assuming they were not cut down by childhood diseases, etc.) to where a 'good long life' was considered living to the age of 70 or 80 (Psalm 90:10).
Much like the belief that God (re)created the world in six days in Genesis 1, it's easy today to be skeptical that the pre-flood patriarchs lived an average of more than 800 years. But, if we remember that an all-powerful, all-knowing God could have remade the world faster than we could snap our fingers, we should not think the information in Genesis is so far-fetched.
Ultimately, it comes down to belief, a reasonable but not blind faith. If the Bible is reliable in what can be checked, it's reasonable to believe in what cannot be checked. It's much like questioning a witness in a court room during a trial.
If the witness' story checks out in parts that can be checked, and is not contradictory, etc., then it's reasonable to believe his or her testimony on matters that cannot be verified. This explanation of pre-flood lifespans may not seem fully plausible to our rationalistic minds, but that is where faith comes in.