As the other post gives a simple example on the methodology here a bit more about the necessity of this science and how scholars describe it.
Imam Sufyan a-Thawri has given a simple explanation on how one verifies a narrator saying:
All translations in this post are my tranlation from Arabic take them carefully!
قال سفيان الثوري : لما استعمل الرواة الكذب استعملنا لهم التاريخ (See for example in ibn 'Asakirs Tareekh Dimashq تاريخ دمشق)
Sufyan a-Tharwi said: When the narrators start using lies we started using history against them.
This statement means that the scholars of hadith used all accesible information about a narrator, birth place, birth date, date of death, tribe, parents name, biography, teachers, students, mates to verify whether or not there was a meeting between a narator and the person he narrated from.
Similar statement came from other scholars:
سمعت حسان بن زيد ، يقول : لم نستعن على الكذابين بمثل التاريخ نقول للشيخ : سنة كم ولدت ؟ فإذا أقر بمولده عرفنا صدقه من كذبه . (Same source as above see here)
Hassan ibn Zayd said: we didn't rely on anything against the liars more than on the history, we asked the sheiekh: when were you born? If he approaved it we knew his truth or lie.
This statement shows that history in this context in first place seems to refer to the date of birth of a narrator.
There is also the statement of imam as-Sakhawi أبو عبد الله محمد بن عبد الرحمن السخاوي in his commentary called Fath al-Mughith on the poem of the imam and hadifh al-'Iraqi called al-Alfiyah (see here) in the chapter abou the history/biography (dates of birth) of the narrators:
تواريخ الرواة والوفيات فنٌّ عظيم الوقع من الدين، قديم النفع به للمسلمين، لا يُستغنى عنه.
The histories (date of births) of the narrators and their date of death are an art with a great impact on the religion, it is of old benefit (and use) for the Muslims and one cannot dispense with it.
So for knowing or identifying a rawy (narrator) we need to check his biography. Therefore we find that most hadith scholars have also been known as authors of biographies or history books.
Hadith scholars therefore compiled special books covering names of narrators and all possible indicators to identify them: Place of birth, place of work, date of birth, date of death, names, surnames, kunyahs, etc. this helps to identify a narrator.
In Imam a-Dhahabi's Siyar 'Alam an-Nubala' سير أعلام النبلاء (the biographies of the Knowlegdable of the nobles) for example we often find among the information presented: The full name inculding fathers and grandfathers name if avalable, mothers name if available etc. we also find the names of the teachers, the names of the students, some quotes or statements of the person presented and some quotes of poeple who witnessed him/her etc. and quotes of hadith narrations of the person if it was a muahaddith.
Based on this information one can start investigating.
There are many other books like the three Tarikh's (Histories) of imam al-Bukhari, many scholars have even listed weak narrators in boooks entitled a-Do'afaa' etc.. Also among the boooks one could rely on you may find al-Mizzi's يوسف بن عبدالرحمن المزي Tahdyb al-Kamal تهذيب الكمال, ibn Sa'ads ابن سعد at-Tabaqaat al-Kubra (The great classes) one of the earliest classifications of narrators based on categories (sahabah/companions, tabi'yn/followers, tabi' at-Tabi'yn/the followers of the followers, the imams etc.), imam an-Nasa-i had also a book called at-Tabaqaat.
From the above it is clear that this is primarily a matter of Ijtihad and it is not an easy matter. As much of these information might not be available for any of the narrators. And often one can't confirm a meeting between a narrator and another even if they lived at the same time.
My major source is beside this fatwa and this article on islamweb -both in Arabic language-.