One of the readers has taken pains to get a reference text in Mysuru, published in the year 1900!My gratitude to him. I am providing the communication from him
As to the methods, though in essence the same, there are minor differences in detail so that people of different dispositions may follow.
Hinduism understands that there are as many dispositions as are Human Beings, they have tried to suit the groups these texts to suit the groups which have common dispositions.
Each Veda has four parts.
Samhitas are hymns addressed to Gods.
The Samhitas and the Brahmanas form the Karma-Kanda segment of the Vedas.
They are concerned with the ceremonial rites and rituals.
Aranyakas are concerned more with knowledge ,Gnana and this is mainly for the semi retired from day to day activities.
These are the basics of Gotra, Shaka and Sutra link.
If one finds it difficult,one may trace them if they have any of the three, that is Gotra, Shaka, Sutra.
And over a period of years Brahmins have started using their professions as their surnames ,as against the Hindu practice of using Sharma as their surname and for indentification their Pravara/Abhivadan Mantra.
So when one has a surname like Upadhyaya it merely denotes the profession and not a caste.
To find it one has to check the Pravara.
Reason is that many Rishis have more than one wife and many children through each of them.
Kasyapa had more than one wife.
The Prajapati Daksha gave his thirteen daughters (Aditi, Diti, Kadru, Danu, Arishta, Surasa, Surabhi, Vinata, Tamra, Krodhavasha,Idā, Vishva and Muni in marriage to Kashyapa.
Though the Father is one, mother is different.
Rama and Krishna, though Avatras of Vishnu were born to Human beings and as such they had ancestors to whose lineage they belonged to.
This is yet another instance of Hinduism treating Gods as Huan Beings and not some one special when they lived, their ancestors were given the respect due to them.