Actually we have many new years. There is the agriculture new year and there is the civil new year, then there is the roman new year the rest of the world goes by and is secular so most of us celebrate it in one form or another, except for the Ultra Orthodox.
Tishri 1 is called Rosh Hashanah which means Head of the year and it starts on the first day of the month, unlike all other festivals, Rosh Hashanah is on the new moon the first day. So it can be determined when this is but only traditionally by the Aviv month, the month in spring which is determined by the barley, as it is important to keeping the feast of unleavened bread.
Aviv, or the babylonian name, Nissan, has three feasts actually
, First comes Passover which happens on the changing of the 14th to the 15th of Aviv, the next day is ( starting at sundown on the 15th) unleavened bread and it followed on the 16th by first fruits, this is very important when figuring in Messiah in these festivals.
What we call our civil calendar now was introduced by G-d from Genesis to Exodus 12, he changed it in Exodus 12:1. A good example to see this is in the flood story. This was changed because the moedim or appointed times ( feasts) were being introduced and were contingent on the argicultural cycle which they would be taking up when entering the land, when before they were basically wanderers.