I have read this article, here is some the simplified version.
If a Muslim woman comes to know of a man who has good character and deen and would make a good husband, there is absolutely nothing wrong with approaching him in an honorable way with a marriage proposal.
Some ways that she could do this would be to ask her parents to approach his parents; or to send a message through someone who knows him (for example his sister, aunt, cousin, etc) that she is interested, in order to learn if he also might be interested. She can also approach him directly and raise the subject, as long as she follows Islamic rules of etiquette (meeting in public, having a chaperone, no flirtatious or sexual speech, lowering the gaze, etc).
This may be seen as improper or brazen in some cultures. But that is a cultural attitude, not an Islamic one.
Let us look to the Prophet Muhammad (pbuh) as our example, since the Quran says, “There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often.” (33:21)
First of all, he accepted a proposal from a woman, Khadijah (RA), who became his wife. It’s true that he had not yet been appointed as a Prophet at that time nor was the Quran revealed; however, he was protected by Allah from sin from the time of his birth. Allah would never have permitted him to accept a proposal from a woman if doing so was in any way shameful or improper.
Consider this incident, narrated in Al-Bukhari, Volume 7, Book 62, Number 54:
Narrated Sahl bin Sad:
A woman presented herself to the Prophet (for marriage). A man said to him, “O Allah’s Apostle! (If you are not in need of her) marry her to me.” The Prophet said, “What have you got?” The man said, “I have nothing.” The Prophet said (to him), “Go and search for something) even if it were an iron ring.” The man went and returned saying, “No, I have not found anything, not even an iron ring; but this is my (Izar) waist sheet, and half of it is for her.” He had no Rida’ (upper garment). The Prophet said, “What will she do with your waist sheet? If you wear it, she will have nothing over her; and if she wears it, you will have nothing over you.” So the man sat down and when he had sat a long time, he got up (to leave). When the Prophet saw him (leaving), he called him back, or the man was called (for him), and he said to the man, “How much of the Quran do you know (by heart)?” The man replied I know such Sura and such Sura (by heart),” naming the Suras The Prophet said, “I have married her to you for what you know of the Quran.”
As we can see, a woman approached the Prophet (pbuh) for marriage and he did not disapprove of that or criticize her. He personally did not wish to marry her, so he matched her with someone else and married them to each other.
Furthermore, a general rule in Islamic fiqh is that all things are halal unless they are specifically prohibited by Quran or Sunnah. And there is nothing in Quran or Sunnah that would suggest that it is prohibited for a woman to initiate a marriage proposal. And Allah knows best.
It is perfectly fine for you to approach the young man in a most honorable way and let him know your intentions by hinting or being flat out about it, depending upon the noble custom in your society. This is not prohibited by Islam.
Unfortunately, however, there remains a stigma within certain Muslim cultures against a woman’s family proposing or initiating marriage talks. It is likewise considered rude and offensive for the daughter to suggest a suitable man to her parents which, in some cases, is automatically deemed to mean that she is involved in an illicit relationship with him.