The Hindu dating systems follows one of the two popular models, the विक्रम सम्वत्  which originated in 58BCE  or the शाक सम्वत् which originated in 78 CE. (सम्वत् means year ). Prior to these an even more ancient system was used in Mauryan empire and ancient India. This was known as the सप्तर्षि calendar (estimated origin 6626 BCE)

The शाक calendar is believed to be of Indo-Scythian origin, the Vikram calendar originates at the time King Vikramaditya defeated the Shaka king and became the king of the famous Indian city of Ujjain.

Both calendars use dating systems that start with the the month of चैत्र which starts anytime between March 22 to April 14 depending on whether the solar model is used or the lunar model. Depending on where you are in India either the solar, lunar or lunisolar systems are popular. 

The months go as follows

 चैत्र – start of year in spring

वैशाख – spring month

ज्येष्ठ – summer

आषाढ – Summer

श्रावण – monsoon

भाद्रपद – monsoon

अश्विन – autumn (fall)

कार्तिक – autumn

मार्गशीर्ष – winter

पौष – winter

माग – winter

फाल्गुन – warming of temperature

The lunar calendar comprises of two fortnights known as पक्ष – the waxing phase of the moon शुक्ळपक्ष and the waning phase कृष्णपक्ष

शुक्ळपक्ष – अमावास्या (no moon day) to पौर्णमी / पूर्णिमा (full moon day)

कृष्णपक्ष – पौर्णमी to अमावास्या

Total days in a Hindu lunar year therefore is about 354 days and 8 hours

The Hindu solar year goes by the traversal of the earth around the sun which is about 365 days and 6 hours as per the solar calendar.

To sync the lunar to the solar calendar every three years a lunar month called अधिमास is added to the lunar calendar. This month is considered inauspicious and prayers to पुरुषोत्तमः or Lord Vishnu  are conducted.