The Wagha/Attari border is the only place you can officially cross from Pakistan into India, and travelers usually make the trip between the Punjab’s two major cities: Lahore in Pakistan and Amritsar in India.
In order to cross the border from into India from Pakistan, you need to have valid visas for both countries. If you are planning to return to Pakistan, make sure that you have another entry left on your visa before you leave the country, unless you are planning to apply for a new Pakistan visa in New Delhi.
There are often buses that go straight from Lahore to New Delhi, and sometimes there is a train service operating across the border, but these services are vulnerable to the state of government relations between the neighboring countries. Not only that, services that join the two countries directly are seen as symbols of friendship and cooperation, and these services are accompanied by heavy police escorts due to the fact that not everyone thinks friendship and cooperation are the best policies to pursue. It’s safer and faster to stick with local transportation on each side of the border rather than to use a special service that operates between the two countries.