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Navaratri is a festival dedicated to the worship of the Hindu deity Durga. The word Navaratri means ‘nine nights’ in Sanskrit, nava meaning nine and ratri meaning nights.During these nine nights and ten days, nine forms of Devi are worshipped. The tenth day is commonly referred to as Vijayadashami or “Dussehra” . Navaratri is an important major festival and is celebrated all over India and Nepal. Diwali the festival of lights is celebrated twenty days after Dussehra. Though there are total five types of Navaratri that come in a year, but Sharad Navaratri is the most popular one. Hence, the term Navaratri is being used for Sharada Navaratri here.
In India different states have different rituals:

-West Bengal  they are celebrated as Durga Puja.

-Punjab, Navaratri is known  Naratey where the first seven days are for fasting. On the eighth day or Ashtami, devotees break their fasts by calling young girls home and these girls are treated as the goddess herself. They are called “Kanjak Devis”.

– Gujarat and Mumbai, Navaratri is celebrated with the famous Garba and Dandiya-Raas dance.

– Goa, the idol of the goddess is put in a specially-decorated colourful swing and for nine nights, this swing is being swung to the tune of temple music (called as ranavadya).

-Tamil Nadu, people set up steps and place idols on them. This is known as golu.

-Karnataka, Ayudha Puja, the ninth day of Mysore Dasara, is celebrated with the worship of implements used in daily life such as computers, books, vehicles, or kitchen tools.

– Andhra Pradesh, people celebrate Bathukamma festival over a period of nine days.

Source:Wikipedia