Hebrew civil years, which begin in the Spring, consist (usually) of twelve months. These months are Abib (Nisan) with 30 days, Iyar (29 days), Sivan (30 days), Tammuz (29 days), Ab (30 days), Elul (29 days), Tishri (30 days), Heshvan (29 or 30 days), Kislev 29 or 30 (29 or 30 days), Tebeth (29 days), Shebat (30 days) and Adar (29 days).
There are several types of years in the Hebrew (Biblical) calendar. A deficient common year contains 353 days, a regular common year contains 354 days and a perfect common year contains 355 days. An intercalary or leap year is one where a thirteenth month, called Adar 1, is added. Leap years can be composed of 383, 384 or 385 days.
Why New Moons were important
Some ancient Israelites observed something called New Moons. When a New Moon occurred (roughly every 29 days) the people used the day not only to mark time but also to rejoice before God. King Saul, the first human king over a united Israel, held special meals or banquets on these days (1Samuel 20). New moons featured prominently in the Old Testament and even in the New Testament.
In today's world we are not likely to lose our calendars. With computers, the Internet, cable and broadcast television, radio, newspapers, watches, cell phones, iPads and so on we can know (whenever we wish) the year, month, date and time with incredible accuracy. In biblical times, however, this was not so. Faithful observance of each new moon was required so that the calendar would never become corrupted. To people in the Bible new moons were their calendars.
When Greeks and other nationalities came into the church during Roman times, how would they have known WHEN to observe the Holy Days? They couldn't buy a calendar. Without observing (taking note of) the new moons they would have NO IDEA when to observe the Feast days.
The fact that the apostle Paul mentions these days in Colossians 2:16 does not mean they were commanded for the entire church or even the Colossians themselves. They needed to keep a diligent track of the new moons since no one else in their society was going to do that for them. To keep track of the new moons in Biblical times was a way of accurately knowing the passage of time. It was absolutely essential for keeping track of dates IF one wanted to know when the seventh new moon of the year (i.e. the Day of Trumpets), as well as all the other Holy Days, would occur.
New Moons in the Real World
The difficulty arising with observing these days comes from the fact that the moon appears differently to different parts of the world. Would we observe these days when the new moon occurs over Jerusalem? Or would we observe the days of the actual invisible new moon conjunctions as our "new mondays"? Or would our observance be based on when this celestial event occurred in OUR part of the earth? For example, the weekly Sabbath is observed based on the time at which the LOCAL sunset occurs. So would we observe new moons "as they come to us," with the result that people in different parts of the world would observe them on different days of the Roman calendar?
The Day of Trumpets is a new moon day. So IF we were to observe new moons based on when they occur in our locality, then we would end up keeping the Day of Trumpets (and therefore also the Feast of Tabernacles) on different days from other people in different areas of the world.
In conclusion, we do not have to observe the new moons today for the below reasons.
There is NO commands anywhere in the Bible to observe new moons in a religious manner.
There are NO instructions or guidelines on how the Biblical new moons should be observed
Leviticus chapter 23 carefully lists ALL the days in the year God expects us to observe in a religious manner. New moons simply are not listed!
Inferences from references to new moons during the millennial reign of Jesus Christ on earth are not clear indications for what we today should be doing.
Observing these days in biblical times is very understandable. It was the only way people could keep an accurate track of the passage of time. Carefully taking note of the phrases of the moon was the equivalent of people having a watch which also displays the date and the day of the week. If people during the rule of Christ observe new moons the conditions will no doubt be different as every month will be perfect - meaning no adjustments needed.