The best way to reach Amman is to fly there, though you can also fly to Israel, cross the border and drive from there.
The best way to go from India would be to take a flight from your desired Indian city to Amman. There are numerous options available from all the major towns in India.
Queen Alia International Airport at Zizya is 30 kilometres from Jordanês capital Amman, and King Hussein International Airport at Aqaba are the two airports in Jordan. Regular flights are available from international airports such as New Delhi, Chennai, Bangalore, Mumbai, Pune, Kochi, Kolkata, Jaipur to Amman and Aqaba as well. Air Arabia, Oman Air, Gulf Air, Kuwait Airways, Jet Airways, Etihad Airways, Emirates, Turkish Airlines, Lufthansa, Air Arabia, Royal Jordanian Airlines, Air India, Egypt Air fly from India to Jordan. If coming from Israel, flights from India mostly land at Tel Aviv Yafo in Tel Aviv. Connecting flights are available to Eilat.
You may bring your own vehicle should you wish to do so but you must have papers allowing you to pass through, your own insurance, the registration papers of the vehicle and your national license. You also have to take a local insurance. Privately hired taxis will also drive you across the border from neighbouring countries, but the visa to Jordan must be obtained beforehand. Car rentals are available and details are provided on the Jordanian Embassy website. If coming from Israel, the best option is to cross at the South Israeli Arava Border near Eilat.
The Hejaz Railway Line runs from Damascus to Amman
Bus services ply to Amman from Damascus, Cairo, and Istanbul, though you will have to fly to those cities first
You may take a ship till the Aqaba port from countries such as Egypt, and then drive or take a flight to Amman
Busses and taxis are the most used transport options available in the city. Car rental companies are plenty in number.