I had barely settled into my lodgings in the city of Udaipur, in southern Rajasthan, when the proprietor was at the door. Mr Singh, a congenial man, had acquired a rueful urgency. Something had happened, he told me. Something big, and, well, he was going to need to ask me to stay for two months – at this, he looked most apologetic – and to pay the corresponding rent upfront. But only because he had to be sure that I remained in place.

I bit my tongue. I was in India to learn Hindi, and staying in Mr Singh's haveli, or mansion, as what Indians call a "paying guest" – combination lodger and honoured, if shoehorned-in, family member – so had an obligation to hear my newly transfigured relative out. I stared at him levelly. He rushed to explain.

"The reason is, last night I have got the proposal for my daughter." A marriage offer for Puja, his oldest. His smile was barely contained.

"The boy is a lawyer from a Rajput family." Good job, same cast. "It is 99.99% certain."

The pandit (Hindu wise man) just had to weigh in and it'd be a go – so long, he continued, in the nicest manner possible, as I didn't screw it up. They'd had the call the night I'd moved in. Clearly, I was auspicious and had, through cosmic machinations known only to the gods, brought on this happy event. Which meant that if I left before negotiations were complete, the whole thing could topple, and I could scotch little Puja's dreams.

By that point, I'd been a paying guest in several homes, and knew the ropes. I performed fast calculations in my head. With his claim that I was auspicious to the proceedings Mr Singh was, by Indian reckoning, on firm grounds. But demanding two months' rent in advance, while ingenious, was over the top.

No, no, no, I repeated sternly, and went on to have a lovely stay. I had the run of what had been the women's quarters in the Singhs' ancient haveli, with 17th-century murals of tiger hunts adorning the walls. In the afternoons, stained-glass windows threw confetti of light across the gleaming marble floors.

In the mornings, Mr Singh would bring me breakfast and stories from the old days: "In my grandfather's time, men and women could not sleep together. The laws were very strict. My grandmother slept upstairs. So my grandfather made a hole in the ceiling and, late at night, pulled her through."

The arrangements were spectacular and spectacularly serene, and with meals, came to about £5 a night.

With some judicious navigation, more of which below, staying as a paying guest can be a terrific way to visit India. Though little-known outside the subcontinent, the system has existed there for years and can be found in most towns and cities. They're low-rent, literally – though because they offer a full-on experience of Indian family life, which is almost always rollicking – they usually come with some Bollywood-level drama thrown in.

The idea of paying guests began with parents who wanted lodging and family supervision for a son or daughter in an out-of-town university or working in a distant city, but didn't have any actual relatives in the area. Someone usually knew someone who had a spare room and, over time, a nationwide system grew up.

For Indian families the parental supervisory element is paramount, which is why rates are often quoted by the month – though nightly arrangements can generally be negotiated. Over they years, though, young Western travellers and seasoned India hands have discovered that many of these spare rooms are fairly luxurious, and that a homestay can provide an unparalleled immersion into the culture.

In recent years, as India continues to blaze white-hot as a tourist destination, and high prices put hotels of all kinds beyond the reach of many travellers, paying guest homes have become an increasingly attractive alternative.

Although you are expected to abide by family rules, it has been my experience that for westerners, the rules are negotiable. I put up for a while with an extended Jain family, who requested that I be in by 9pm every night – Jains tend to be early to bed. But eventually they graciously gave me a key, and leave to come and go as I pleased.

Because you're living in close quarters with a family whose cultural orientation is probably very different from your own, a certain amount of tolerance is required. At the Jain family, I enjoyed ambrosial vegetarian meals, a sunken ensuite marble bath, and instant fashion checks whenever I went out. The wives frowned on cross dressing – mixing salwaar kameez tops with Western skirts. When I stayed with an Indian thukrani-sa, or countess, I had lavish breakfasts and the eye-popping experiencing of getting to rummage with her through her family jewels. She'd toss me thick gold collars with rippling bibs of diamonds to try on, gold bracelets with clasps carved like elephant heads. "… and this one I got by trading milk cows," she'd say.

Not all my forays have been successful. There was the time I moved in with a family called the Bhatts, whose lovely 17th-century home revealed itself to be booby-trapped. The first morning, at 5am, a metallic slamming started up somewhere in the bowels of the building, but Mr Bhatt insisted the noise was a figment of my imagination.

While at the Singhs I got to witness at first hand the calculations that go into arranging an Indian wedding. Mr Singh would return from visits to the other family, in Ahmedabad, with complaints that they were bargaining "like vegetable sellers".

"They said they wanted women in the procession. I said no. They wanted 40 people. I said no, I could not. They wanted first-class tickets, and aircon, for everyone to come here. I said no."

Wherever I stayed, though, my Hindi blossomed, in ways that it might not have otherwise. I learned how to say "son of a bitch". And one night, when Mrs Singh was on a roll, I learned how to say "I love you" in four different ways.

• Katherine Russell Rich is the author of Dreaming in Hindi: Life inTranslation, published by Portobello Books, price £12.99