Should he tell a non-Muslim all the details of Islam?

Yes, it is right to tell him what Islam means, but it is not wise to tell him all the details of Islam in one go. Hence the daa’iyah has to exercise wisdom and start with the most important things and understand the priorities of da’wah. It was narrated in the hadeeth of Ibn ‘Abbaas (may Allaah be pleased with him) that when the Messenger of Allaah (peace and blessings of Allaah be upon him) sent Mu’aadh (may Allaah be pleased with him) to Yemen, he said: “You are going to some of the People of the Book, so let the first thing to which you call them be the worship of Allaah alone. Then when they have learned about Allaah, tell them that Allaah has enjoined upon them five prayers each day and night. After they do that, then tell them that Allaah has enjoined upon them the zakaat to be paid from their wealth and given to the poor. If they obey, then take that from them, but leave the best of their wealth.” 

(Narrated by al-Bukhaari, 1458; Muslim, 19) 

The Muslim is obliged to call others to Islam, on condition that he knows what he is calling them to, so that he will not make mistakes in his da’wah. Allaah says (interpretation of the meaning): 

“Say (O Muhammad): ‘This is my way; I invite unto Allaah (i.e. to the Oneness of Allaah — Islamic Monotheism) with sure knowledge, I and whosoever follows me (also must invite others to Allaah, i.e. to the Oneness of Allaah — Islamic Monotheism with sure knowledge). And Glorified and Exalted be Allaah (above all that they associate as partners with Him). And I am not of the Mushrikoon (polytheists, pagans, idolaters and disbelievers in the Oneness of Allaah; those who worship others along with Allaah or set up rivals or partners to Allaah)’”

[Yoosuf 12:108]

Baseerah (translated here as “sure knowledge”) means the knowledge with which truth may be distinguished from falsehood.” 

(From Tafseer al-Baghawi, 4/284). 

Ibn Katheer (may Allaah have mercy on him) said in his Tafseer (4/422) in his commentary on this aayah: “Allaah is telling His slave and Messenger to the two races of mankind and the jinn to tell the people that this is his way and his path, which is calling them to bear witness that there is no god except Allaah alone, with no partner or associate, calling them to Allaah in this way with sure knowledge, certain faith and shar’i and rational proof.” 

You should note that calling people to Islam is obligatory. Our scholars (may Allaah have mercy on them) said: “It is obligatory upon every Muslim and Muslimah to know four things and act upon them: 

1 – Knowledge, which means that the slave knows his Lord and his Prophet, and knows the religion of Islam based on evidence.

2 – Acting upon it, which means that he should act upon this knowledge.

3 – Calling others to it, i.e., calling them to what he has learned.

4 – Patiently bearing any difficulties encountered as a result of seeking knowledge, acting upon it and calling others to what he has learned. 

The evidence for these four things is the verse in which Allaah says (interpretation of the meaning): 

“By Al-‘Asr (the time).

Verily, man is in loss,

Except those who believe (in Islamic Monotheism) and do righteous good deeds, and recommend one another to the truth [i.e. order one another to perform all kinds of good deeds (Al-Ma‘roof) which Allaah has ordained, and abstain from all kinds of sins and evil deeds (Al-Munkar) which Allaah has forbidden], and recommend one another to patience (for the sufferings, harms, and injuries which one may encounter in Allaah’s Cause during preaching His religion of Islamic Monotheism or Jihad)”

[al-‘Asr 103:1-3]

The phrase “Except those who believe” refers to the first issue, because there is no faith or belief without knowledge. The phrase “and do righteous good deeds” refers to the second issue. The phrase “and recommend one another to the truth” refers to the third issue, which is da’wah. And the phrase “and recommend one another to patience” refers to the fourth issue. 

So you should explain to the non-Muslim what the religion of Islam means, namely submission to Allaah, accepting His commands, and believing in His Prophet (peace and blessings of Allaah be upon him). You should tell him about the beauties of Islam (see question no. 219) so that he will be convinced of Islam and will accept it. If he becomes Muslim, then tell him about the rulings of Islam in detail, explaining it to him gradually, according to his level of understanding. Do not discuss with him things that may cause him to doubt or overwhelm him with too much information. But follow the method of the rabbaaniyeen of whom Allaah says (interpretation of the meaning): 

“Be you Rabbaaniyyoon (learned men of religion who practise what they know and also preach others), because you are teaching the Book, and you are studying it”

[Aal ‘Imraan 3:79]

It was said that the rabbaaniyyoon are those who teach people by starting with easy and straightforward issues before they present them with complicated issues. (Tafseer al-Baghawi, 2/60)

 i.e., the major principles and issues before the finer details and minor issues. And Allaah is the Guide to the straight path.