The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.
For the rest of us, there are plenty of easily accessible computer programs that will calculate the Jewish calendar for more than a millennium to come. Note that the number of days between Nissan and Tishri is always the same.
When the Sanhedrin heard testimony from two independent, reliable eyewitnesses that the new moon occurred on a certain date, they would declare the rosh chodesh (first of the month) and send out messengers to tell people when the month began.
The problem with strictly lunar calendars is that there are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar is about 11 days shorter than a solar year and a 13-month lunar is about 19 longer than a solar year.
Years are either 12 or 13 months, corresponding to the 12.4 month solar cycle.
The lunar month on the Jewish calendar begins when the first sliver of moon becomes visible after the dark of the moon.