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Refer Uma Shankara Samvada
Eligibility to Grhasthashrama
According to Manusmrti,
वेदानधीत्य वेदौ वा वेदं वापि यथाक्रमम् । अविप्लुतब्रह्मचर्यो गृहस्थाश्रमं आवसेत् । । ३.२ । ।
vedānadhītya vedau vā vedaṁ vāpi yathākramam । aviplutabrahmacaryo gr̥hasthāśramaṁ āvaset । । 3.2 । ।
Meaning: (A student) who has studied in due order all the Vedas, or two, or even one only, without breaking the (rules of) studentship, shall enter the order of householders.
गृहस्थधर्मः ॥ Grhastha dharma
A householder uses five things frequently in his daily life viz. the hearth (floor of fire place), the grinding-stone, the broom, the pestle and mortar and the water-vessel. And while doing so he incurs sin since each of these five are potentially harmful for small living organisms that are invisible to the naked eyes. Hence, they are called slaughter-houses. In order to successively expiate the offences committed by means of all these five tools, the great sages have prescribed for householders the daily performance of the five great sacrifices. (Manu. 3.68 and 69) It is said,
स्वाध्यायेनार्चयेत र्षीन्होमैर्देवान्यथाविधि । पितॄञ् श्राद्धैश्च नॄनन्नैर्भूतानि बलिकर्मणा । । ३.८१ । ।
svādhyāyenārcayeta rṣīnhomairdevānyathāvidhi । pitr̥̄ñ śrāddhaiśca nr̥̄nannairbhūtāni balikarmaṇā । । 3.81 । ।
Meaning: Let him (the Grhastha) worship, according to the rule, the sages by the self study/recitation of the Veda, the gods by burnt oblations, the manes by funeral offerings (Shraddha), men by (gifts of) food, and the Bhutas by the Bali offering.
Also called as Ahuta, it refers to the sacrifice offered to the brahman in the form of teaching and studying the vedas - अध्यापनं ब्रह्मयज्ञः | adhyāpanaṁ brahmayajñaḥ. Here, the offering is not given into the fire, rather it is in the form of chanting of vedic texts - जपोऽहुतो | japo'huto | (Manu 3.70 and 3.74)
Also called as Prashita, it refers to the sacrifice to pitrus done with the offerings of water and food called tarpana - पितृयज्ञस्तु तर्पणम् । pitr̥yajñastu tarpaṇam. The term Prashita literally means 'eaten'. It is a daily oblation to Pitrus - प्राशितं पितृतर्पणम् । prāśitaṁ pitr̥tarpaṇam । (Manu 3.70 and 3.74)
Also called Brahmya-huta, the respectful reception of guests - ब्राह्म्यं हुतं द्विजाग्र्यार्चा | brāhmyaṁ hutaṁ dvijāgryārcāis |, the Nruyajna refers to the hospitality offered to guests - नृयज्ञोऽतिथिपूजनम् | nr̥yajño'tithipūjanam । (Manu 3.70 and 3.74)
According to Manusmrti, an oblation duly offered into the fire, reaches the sun; from the sun comes rain, from rain food, there from the living creatures derive their subsistence (3.76) Hence, it says,
स्वाध्याये नित्ययुक्तः स्याद्दैवे चैवेह कर्मणि । दैवकर्मणि युक्तो हि बिभर्तीदं चराचरम् । । ३.७५ । ।
पञ्चैतान्यो महाअयज्ञान्न हापयति शक्तितः । स गृहेऽपि वसन्नित्यं सूनादोषैर्न लिप्यते । । ३.७१ । ।
देवतातिथिभृत्यानां पितॄणां आत्मनश्च यः । न निर्वपति पञ्चानां उच्छ्वसन्न स जीवति । । ३.७२ । ।
svādhyāye nityayuktaḥ syāddaive caiveha karmaṇi । daivakarmaṇi yukto hi bibhartīdaṁ carācaram । । 3.75 । ।
pañcaitānyo mahāayajñānna hāpayati śaktitaḥ । sa gr̥he'pi vasannityaṁ sūnādoṣairna lipyate । । 3.71 । ।
devatātithibhr̥tyānāṁ pitr̥̄ṇāṁ ātmanaśca yaḥ । na nirvapati pañcānāṁ ucchvasanna sa jīvati । । 3.72 । ।
Meaning: Let (every man) in this (second order, at least) daily apply himself to the private recitation of the Veda, and also to the performance of the offering to the gods; for he who is diligent in the performance of sacrifices, supports both the movable and the immovable creation. He who neglects not these five great sacrifices, while he is able (to perform them), is not tainted by the sins (committed) in the five places of slaughter, though he constantly lives in the (order of) house holders. But he who does not feed these five, the gods, his guests, those whom he is bound to maintain, the pitrus, and himself, lives not, though he breathes. 
कर्तव्यनिवृत्तिः ॥ Retirement from Duties
According to Manusmrti, when one has paid, according to the law, one's debts to the great sages, to the forefathers, and to the gods, one should make over everything to one's son and dwell (in the house), not caring for any worldly concerns. [v.4.257.]
महर्षिपितृदेवानां गत्वानृण्यं यथाविधि । पुत्रे सर्वं समासज्य वसेन्माध्यस्थ्यं आश्रितः । । ४.२५७ । ।
maharṣipitr̥devānāṁ gatvānr̥ṇyaṁ yathāvidhi । putre sarvaṁ samāsajya vasenmādhyasthyaṁ āśritaḥ । । 4.257 । ।
At this stage, one is advised to constantly meditate in solitude on that which is salutary for one's soul; for one who meditates in solitude attains supreme bliss. [v.4.258.]
एकाकी चिन्तयेन्नित्यं विविक्ते हितं आत्मनः । एकाकी चिन्तयानो हि परं श्रेयोऽधिगच्छति । । ४.२५८ । ।
ekākī cintayennityaṁ vivikte hitaṁ ātmanaḥ । ekākī cintayāno hi paraṁ śreyo'dhigacchati । । 4.258 । ।