Our primary sources for this explanation are "Things To Come" by J. Dwight Pentecost and "The Coming Prince" by Sir Robert Anderson.
Our point of reference is Daniel 9:25-26 where it's said:
"So you are to know and discern that from the issuing of a decree to restore and rebuild Jerusalem until Messiah the Prince there will be seven weeks and sixty-two weeks. After the sixty-two weeks Messiah will be cut off."
Now; a technicality to be aware of is that those sixty-nine weeks are not heptads of days, rather, of years; which when added up come to 483.
A further technicality to be aware of is that those 483 years aren't normal years, rather, they're prophetic years, which are only 360 days apiece compared to normal years which are roughly 364¼ days apiece.
So, in normal years, the sixty-nine weeks add up to only 477.
Turning to Neh 1:1-2:18, we find our hero depressed and upset because his home town, the very city where his relatives are buried, was in ruins; its wall broken down, and its gates ashes. So, with a goodly amount of butterflies in his stomach, Nehemiah petitioned his boss for a leave of absence to go and rebuild Jerusalem.
Artaxerxes gave him permission, supported by official memorandums, in the month of Nisan, in the twentieth year of his reign. So it is in Neh 2 that we find the only actual Bible record of a royal permit to rebuild the city of Jerusalem. This, then, is our choice for the beginning of Daniel's prediction.
[ If perchance someone out there feels like computing Messiah's first visit on their own, just be sure to begin your dating with the commission to rebuild the city of Jerusalem rather than the Temple because those two projects weren't taken up simultaneously.]
Fortunately, the date of Artaxerxes reign can be easily and definitely ascertained-- not from the elaborate investigative treatises of biblical commentators and prophetic writers; but from ordinary history books. Artaxerxes-- a.k.a. Artaxerxes 1 --reigned from 465-425 BCE.
According to Nehemiah, the Persian edict, which gave him permission to rebuild Jerusalem, was issued during the Jewish month of Nisan in the twentieth year of Artaxerxes. Unfortunately the exact day is not given. It is very possible the decree was dated the 1st of Nisan; but that's not really important as long as we come close enough for practical consideration. The sixty-nine weeks then, within reason, and close enough for our purposes, will therefore be calculated from the 1st of Nisan 445 BCE.
Counting 477 normal years forward from 445 BC drops us off at 32 CE which, if correct, becomes the year that Daniel predicted Messiah would be cut off. That figure appears to be in the ball park; and here's why:
According to Luke 3:1-3, Tiberius was the emperor in Rome when John the Baptist began his public ministry.
Tiberius' reign spanned 14 CE to 37 CE and according to Luke, John's ministry began sometime in 29 CE. Precisely on what day Jesus was baptized by John we don't know for sure, but we do know that he was about thirty years old at the time. (Luke 3:21-23)
Jesus' own ministry ran about three years before he was cut off. So if we add 3 to 29 we get 32 CE.
* We're not trying to prove that Jesus was the Messiah predicted by Daniel 9:25 26. We're only explaining why we believe he's a reasonable candidate due to the fact that his life and times coincide remarkably well with Daniel's time element.