Rigveda Upakarma: Should be done on the day in shraavana where shravana is the star and spans at least from sunrise to mid day.But not in Uttara Ashadha if present during sunrise.
श्रवणे श्रवणायाम् उपाकर्म कुर्वीत आश्वलायन गृह्य सूत्र
Samaveda Upakarma: Should be done on hasta nakshatra on bhadrapada shuklapaksha
प्रौष्ठपदी हस्तायाम् वा श्रवणे श्रवणायां उपक्रमण= गोभिल गृह्य सूत्र
Krishna Yajurveda: i.e. Taittiriyas & Maitrayanis should do on shravistha, dhanistha,(avittam in Tamil),on shraavana month,whether it falls on purnima yukta Pratipada (Pratipat)during sunrise (Telugu- paadyami) or prathama.
Shukla Yajurveda: i.e. Vajasaneyi Kanvas and Madhyandinas do in purnima day if purnima is present up to evening.But if punima and pratipada both are present on next day(para viddha) they should do on previous day when chaturdashi stays in day and then purnima comes after mid day(purva viddha).Under no condition they should do/avoid doing in krishna paksha pratipat or broadly speaking they should finish upakarma before approach of krishna paksha.but they postpone upakarma to the next day if purnima is having Uttara Ashadha nakshatra.
श्रवणे पौर्णमास्यां उपाकर्म =पारस्कर गृह्य सूत्र
Atharva Veda: They do on the day when purnima lasts during sunrise.(udaya vyapini tithi)
If there occurs Eclipse and sankranti when sun enters Leo (masa pirrapu/avani 1st in Tamil) during purnima,the people having upakrama for that day should be finished prior to punima when hasta nakshatra is available(generally shravana shukla Panchami/shashti.and for samaveda,if there is sankramana(purattasi 1st) to kanya in bhadrapada then shraavana month's hasta should be considered.
If shraavana suddha Panchami(hasta) day is having sankramana/sankranti and purnima is having eclipse then upakarma is postponed to Samaveda upakarma day,i'e. bhadrapada hasta nakshatra but only Vajasaneyi Shukla Yajurveda people can do upakarma on the Panchami(hasta) having simha sankramana and avoid upakarma on purnima having eclipse.
The details of upAkarma initially is taken from grhya sutras but as they are short aphorisms, the procedures is given in elaborate in the ritualistic books. Hence respective grhya sutra is to be referred for upAkarma and related rituals.
The whole procedure of upAkarma is very long hence it is not possible to include in the post.
For date calculations:
Nirnaya Sindhu
Dharma sindhu
A detailed procedure could be found in the books like
upAkarma paddhati (for respective veda)
aahnika krama (for respective veda)