You could travel for ten lifetimes and only just scratch the surface of exploring India. Here I'm going to give a brief overview of how to travel in India, and some of my favorite parts of the country.
Absolutely huge, diverse, rich in history and culture, India was always a dream of mine to visit. The size of the country alone makes planning travel there a challenge: how do you decide where to go? While there are endless travel routes in India, I'll go through one of my favorite travel routes, that you could follow to cover a broad swath of the country, and cover some of the basics of how to travel in India.
Mumbai (also called Bombay) is home to one of the country's main international airports, and a great place to start your India journey. Many international flights will arrive in either Mumbai or New Delhi. Mumbai is a great metropolis, and home to many incredible tourist attractions and sites, such as the Gateway of India, the Chhatrapati Shivaji Maharaj Terminus, and the Elephanta Caves, which are on an island and only accessible by boat.
It's important to understand that many people in India are living in extreme poverty, and India is home to some of the most densely populated places on Earth. Slums are prevalent in every corner of this country, including Dharavi, the world's largest slum. You can visit Dharavi on your own, or with a responsible tour company, which will ideally use the funds from your tour to help the economy of Dharavi.
Goa is a state on India's western coast, and I arrived there after taking a 15-hour bus from Mumbai. Goa is known for it's Portuguese influence, hippy beach towns, and Goan cuisine. One of the best parts about India in general is that it's cuisine is different from region to region. You can check out this Lonely Planet article about traveling in Goa for an in-depth guide.
Goa is one of my favorite parts about India, and it's the perfect place to stay in a hippy beach shack, rent a scooter, and spend a few weeks (or months). I met folks from all over the world who have been coming to Goa for years. Some of my favorite towns in Goa include Arambol and Anjuna, even though they can be full of tourists. Here you can find beach-side dance parties that go until the morning hours, cafes, hostels, and guest houses galore. I recommend after you enjoy Goa, take the trip down south to Gokarna, which is in the state of Karnataka. It has a similar vibe to Goa, with less tourists.
After Goa I hopped a 15-ish hour bus across India to arrive at Chennai, on India's western coast. I specifically was going to a Sivananda Yoga Center here, and was staying with a friend. Chennai is in the state of Tamil Nadu, and is known for it's Tamil music and dance. There are beaches, a national park, stunning Hindu temples, and monuments.
Chennai was a brief stop-over, mostly to visit the yoga center, but it was also a good place to start our journey up to Varanasi. All the way up in the northern state of Uttar Pradesh, Varanasi is a city unlike any other. It's known as the "spiritual capital" of India, and Hindus come from all over to bathe in the Ganges river. I couldn't recommend visiting Varanasi more, but I also have to say it was a bit intense, and generally isn't for the faint of heart. Varanasi is the India you probably envision, it's streets are crowded, there are thousands of temples, and its streets are crowded.
Varanasi is known as the city of Lord Shiva, and many Hindus come to Varanasi to cremate their loved ones, or to even come in their old age to die themselves. It's not uncommon to witness public funeral proceedings, with bodies in shrouds being carried through the streets, after being lowered into the Ganges. Public cremations also occur here, and it's possible to witness this sacred and holy process up close. Here is a great guide on traveling in Varanasi.
I recommend doing a sunrise boat tour of the Ganges, which will cost you between $3-$5. Varanasi is also a great place to explore Indian street food, as you'll be hard-pressed to find Western cuisine here. If you're looking for places to stay in Varanasi, here's a list of great hostels.
All the way in the northern India is Rajasthan, the country's largest state. There are many incredible cities to visit in Rajasthan, such as Jaipur and Udaipur, but I landed in Pushkar, after some recommendations from friends, and absolutely loved it. Pushkar borders the Thar Desert, and is set on a sacred lake, where Hindu pilgrims come to bathe. There are hundreds of temples, including the Savitri Temple, which is perched high above the city (pro tip: do this hike at sunset, and also be prepared to see monkeys!). Every night you can watch the holy Hindu ritual of Aarti, which also happens in Varanasi, and there is endless incredible street food. There is tons of reasonable accommodation, including hostels to private rooms. Pushkar is a great place to rent a scooter and drive around the desert.
Because India is so expansive, getting around the country can take a bit of logistical planning. I personally used buses, at the recommendation of a local friend. The website Red Bus is incredibly helpful, and you can book journeys across huge stretches of the country (I was even on a bus for more than 20 hours!) There are different types of buses, and it's important to look at the ratings of the buses and the bus companies. There are also different types of buses, and I highly recommend a sleeper bus for any long journey. Plus, make sure you can find where the bus is picking you up - sometimes these will be pretty hard-to-find locations, like on the side of a highway. You can call the bus company and ask for help if you're a little lost at finding the pick-up location.
Trains are also an option, and are very popular, but can sometimes sell out weeks in advance. This was not ideal for me, as I'm a last-minute traveler, so I didn't take trains all that often. You can also fly around the country, and there are airports all over the place, although this would be the more expensive mode of travel. I did this occasionally, and for places that were quite far from each other, or in instances when buses weren't a good option.
When you're in cities and towns, you can rent scooters, but learn how to safely drive them, as Indian roads can be quite dangerous. You can also take tuk tuks, or auto richshaws, which are small three-wheeled vehicles that whizz around the streets, or use cabs.
Indian food is some of my favorite in the world, and I greatly enjoy the cuisine of the different regions. But due to differences in food handling, there are some very important protocols travelers should follow when eating and drinking in India. Never drink the tap water, do not eat fruits and vegetables that are raw with the skin on them (because of the water they're grown with), and be careful with food from street vendors. While I eventually started eating food from street vendors, I do not eat meat or fish.
You'll also often find people eating with their hands, this is customary and traditional. Some places may have utensils upon request. It is customary to eat with your right hand, and even foods like rice and dhal are eaten without forks.
I definitely recommend you try a thali plate, which will consist of an array of delicious foods in a circle, as well as aloo gobi, anything with paneer (cheese), egg bhurji, and lassi, a sweet yogurt drink.