If someone takes Sanyas, how is he supposed to survive? At which place should he live? What do scriptures say on 'how should a sanyasi live'?
I'm answering this first from the perspective of a Major Purāṇa - Nāradīya Purāṇa or Nārada Purāṇa.
Quoting from Part 1: Chapter 27
If someone takes Sanyas, how is he supposed to survive?
नग्नो वा जीर्णकौपीनौ भवेन्मुंडो यतिर्द्विजः ।। समः शत्रौ च मित्रे च तथा मानापमानयोः ।। २७-९४ ।।
- The Brahmana ascetic may remain naked or wear only a ragged loincloth. He should keep his head completely shaven. He should be impartial to an enemy or a friend and view honor and dishonor with equanimity.
अनिंदितद्विजगृहे व्यंगारे भुक्तिवर्जिते ।। विवादरहिते चैव भिक्षार्थं पर्यटेद्यतिः ।। २७-९६ ।।
- The ascetic should beg for alms only in an uncensured Brahmana household where there is no burning coal and where the people have finished taking food and where there is no quarrel.
भवेत्रिषवणस्नायी नारायणपरायणः ।। जपेच्च प्रणवं नित्यं जितात्मा विजितेंद्रियः ।। २७-९७ ।।
- He should take bath thrice a day and be devoted to Narayana. He should always repeat the Pranava. (The syllable OM). He should subdue the sense-organs and keep his mind under control.
At which place should he live?
एकरात्रं वसेद्ग्रामे त्रिरात्रं नगरे तथा ।। भैक्षेण वर्त्तयेन्नित्यं नैकान्नादीभवेद्यतिः ।। २७-९५ ।।
- The ascetic should stay in a village only for a night and in a town, for three nights. He should maintain himself through alms, but should not take food from one person.
What do scriptures say on 'how should a sanyasi live'?
Further , quoting from Āpastamba Dharma Sūtra: Praśna 2. Paṭala 9. Khaṇḍa 21.
- अथ परिव्राजः || ७ ||
- Now [follow the rules] regarding the ascetic [Samnyāsin].
- अत एव ब्रह्मचर्यवान् प्रव्रजति || ८ ||
- Only after [having fulfilled] the duties of that [order of students] he shall go forth [as an ascetic], remaining chaste.
The meaning of the Sūtra is, that the studentship is a necessary preliminary for the
Samnyāsin. If a man considers himself sufficiently purified by his life in that order,
he may become a Samnyāsin immediately after its completion. Otherwise he may
first become a householder, or a hermit, and enter the last order, when his passions
are entirely extinct.
(See also Manu 6:36; Yajñ. 3:56 - 57.)
- तस्य-उपदिशन्ति || ९ ||
- For him [the Samnyāsin]] they prescribe [the following rules]:—
अनग्निर् अनिकेतः स्याद् अशर्म अशरणो मुनिः |
स्वाध्याय-एवौत्सृजमानो वाचं ग्रामे प्राण वृत्तिं प्रतिलभ्य-अनिहो- ‘अनमुत्रश् चरेत् || १० ||
- He shall live without a fire, without a house, without pleasures, without protection. Remaining silent and uttering speech only on the occasion of the daily recitation of the Veda, begging so much food only in the village as will sustain his life, he shall wander about neither caring for this world nor for heaven.
(Manu 6:33, 42 - 45; Yajñ. 3:58 seq.)
- तस्य मुक्तम् आच्छादनं विहितम् || ११ ||
- It is ordained that he shall wear clothes thrown away [by others as useless].
सर्वतः परिमोक्षम् एके || १२ ||
- Some declare that he shall go naked.
Another [commentator] says, “Some declare that he is free from all injunctions and prohibitions, ie. he need neither perform nor avoid any [particular actions].”- Haradatta.
सत्य अनृते सुख दुःखे वेदान् इमं लोकम् अमुं च परित्यज्य-आत्मानम् अन्विच्छेत् || १३
- Abandoning truth and falsehood, pleasure and pain, the Vedas, this world and the next, he shall seek the ātman.
A Sannyasi must sustain himself by only begging. Since he has forsaken fire he must not cook food for himself. He should not stay in the same place for long. He should be constantly on the move. Only during the rainy season and the winter he is allowed to stay in the same place for a relatively longer period.
He may live one day in a village and five days in a city, but five months in the wintry season. At other times he should live in other places (such as forest, etc.). He should not live in a village for two days (even); should he do so, desires and the rest will arise in him and thereby he becomes fit for hell. He should live like a (harmless) worm on the earth with his mind under control and with no settled place of residence, at the end of the village where there are no persons. He may live in the same place in the wintry season. He should roam about on the earth with one or no cloth, with the one vision (of Brahman) alone, with no desires (of objects), with no condemnation of the actions of the wise and with meditation. That yogin of an ascetic should go about, observing the duties of his order of life, and with the eyes cast on the earth, in pure places. He should not roam about in night, midday or the two twilight periods in which are places void or difficult to be waded through or likely to injure living creatures. He may live for one day in a village, for three days in a town,
A wandering ascetic should wander forth according to the rule, abandoning his relatives and free of possessions. 17 Going into the wilderness, 18 he has his head shaven except for the topknot; 19 wears a loin cloth; 20 resides in one place during the rainy season 21 and wears ochre clothes.
Badarayana Dharma Sutras 2.11.26
Now then the duties of the highest class of itinerant monks – the Paramahamsa Parivrajakas (are as follows): They must sit and lie down on the ground. Those having already taken the vow of chastity etc., should use an earthen bowl or one made of gourd, or a wooden bowl; they should give up lust anger, avarice, infatuation, ostentation, haughtiness, jealousy, attachment to objects, egotism, falsehood and the like. The Sannyasin should stay at one place during the four months of the rainy season and during the remaining eight months wander alone, or with a single companion, aye, a single companion.
Aruni Upanishad Chapter 1
"The ascetic that has attained indifference (to objects), should stay in one and the same place in the rainy season (for four months), and then for (the remaining) eight months should wander alone. Then also the ascetic should not stay in one and the same place for more than a day. Like a deer that does not stay in one place on account of fear, he should not stay in one place. He should not create an attraction (in his mind) that may serve as an obstacle to his going about. He should not cross a stream (by swimming) with his hand, nor ascend a tree, nor witness the festival of a God, nor partake of regal food, nor do the external worship of God. Having discarded all things other than the Self, he should be with his body emaciated by taking food (from each house) like the bees (from each flower). He should not increase the fat (in the body); he should discard ghee like blood. Regarding such royal food as flesh, sandal-coating, etc., as offal, the different tastes as the degraded caste, the cloth as a defiled vessel, the oil-bath as sexual union, the gladdening of a friend as urine, desires as cow's flesh, the country known to him as the outcastes’ place, gold and women as cobra or deadly poison, the place of assembly as the burning ground, the capital of the town as the hell called Kumbhīpāka, and royal food as balls of rice offered to the dead, he should be without any worship of God other than the Self; and having given up all the actions of the world and his own country,
More relevant information can be found in this answer. Quoting few verses from the answer:
Bahudakas are those who carry a triple staff, a water pot, a sling , a shoulder yoke, a water strainer, a bowl, shoes, and a seat; who wear a topknot, a sacrificial string, a loincloth, and an ochre garment; who beg their food from virtuous Brahmin households; and who thus seek the self
Hamsas are those who carry a single staff; who wear a sacrificial string but not a topknot; who carry in their hand a sling and a water pot; who spend only one night in a village and five nights in a town or a sacred bathing place; who perform penances such as the one- and two-day fasts, the krcchra, and the lunar fast; and who thus seek the self.
Paramahamsas are those who carry no staff; who are shaven-headed; who wear a loincloth and a patched garment; whose emblem and conduct are concealed