Many hadith mention the practice of casting lots during the time of the Prophet (may the peace and blessings of Allah be upon him). For example, when deciding which of the wives will accompany the Prophet on a journey, they would cast lots.

Do we know how the casting of lots was done? Were the names pulled from a bowl, for example?

Praise
be to Allah

Firstly: 

Al-Bukhaari (2593) and Muslim (2770) narrated that ‘Aa’ishah
(may Allah be pleased with her) said: When the Messenger of Allah (blessings
and peace of Allah be upon him) wanted to travel, he would cast lots among
his wives, and whichever one’s name was picked, he would take her with him. 

This was due to his (blessings and peace of Allah be upon
him) perfect fairness among his wives (may Allah be pleased with them) and
his kindness towards them. 

Secondly: 

With regard to the way in which the casting of lots was done
by the Prophet (blessings and peace of Allah be upon him), we have not come
across anything that describes it clearly in any hadith, but the scholars
have stated that he used to write the names of the people among whom lots
were being drawn on leaves or the like, and put them in his lap, or in a
vessel, then he would tell someone to take out one leaf, and the one whose
name was drawn was the one who would be chosen. 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

The way in which drawing lots was done was that the names
would be written on things, and a stranger would make the draw; the one
whose name was drawn was the one who would be chosen. 

End quote from Fath al-Baari (1/172). See also: al-Haawi
by al-Maawardi (16/254) 

There is nothing in Islamic teaching to specify a particular
way of drawing lots, so however it is done is permissible. 

Az-Zarkashi (may Allah have mercy on him) said: 

However lots are drawn is permissible. End quote. 


Sharh az-Zarkashi ‘ala Khuraqi
(7/455) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

However lots are drawn, it is permissible, because there is
no particular prescribed way of doing it. So reference should be made to
whatever people agree upon. End quote.


Ash-Sharh al-Mumti‘
(2/55) 

For more information, please see the answer to question no.
102446.

And Allah knows best.