Firstly: 

It is not permissible for a Muslim woman to get married without the permission of her wali (guardian), rather it is essential for her to have a wali who will get her married, because the Prophet (peace and blessings of Allaah be upon him) said: “There is no marriage without a wali.” Narrated by Abu Dawood, 2085; classed as saheeh by Shaykh al-Albaani. And he (peace and blessings of Allaah be upon him) said: “Any woman who gets married without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid.” Narrated and classed as hasan by al-Tirmidhi, 1102; Abu Dawood, 2083; Ibn Maajah, 1879 – from the hadeeth of ‘Aa’ishah. Classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 1840. 

Al-Tirmidhi said, commenting on that: 

This is the principle that was followed by the companions of the Prophet (peace and blessings of Allaah be upon him), including ‘Umar ibn al-Khattaab, ‘Ali ibn Abi Taalib, ‘Abd-Allaah ibn ‘Abbaas, Abu Hurayrah and others. Thus it was narrated that some of the fuqaha’ of the Taabi’een such as Sa’eed ibn al-Musayyib, al-Hasan al-Basri, Shurayh, Ibraaheem al-Nakha’i, ‘Umar ibn ‘Abd al-‘Azeez and others said: There is no marriage except with a wali. This is also the view of Sufyaan al-Thawri, ‘Abd-Allaah ibn al-Mubaarak, Maalik, al-Shaafa’i, Ahmad and Ishaaq. End quote. 

In the answer to question no. 2127 you will find an important summary of the conditions and essentials of marriage, and the conditions to be met by the wali. 

In the answer to question no. 7989 there are further important details concerning the importance of having a wali in order for the marriage to be valid. 

Secondly: 

Allaah has commanded walis to marry off the women who are under their care, and not to mistreat them by preventing them from getting married for no legitimate reason. Allaah says (interpretation of the meaning): 

“And marry those among you who are single (i.e. a man who has no wife and the woman who has no husband) and (also marry) the Saalihoon (pious, fit and capable ones) of your (male) slaves and maid‑servants (female slaves). If they be poor, Allaah will enrich them out of His Bounty. And Allaah is All‑Sufficient for His creatures’ needs, All‑Knowing (about the state of the people)”

[al-Noor 24:32]

Similarly, the Prophet (peace and blessings of Allaah be upon him) commanded walis not to prevent the marriage of the woman whom Allaah has placed under their care if a suitor whose religious commitment and character are good comes to propose marriage. He said: “If there comes to you one with whose religious commitment and character you are pleased, then marry (your daughter or female relative under your care) to him, for if you do not do that there will be fitnah and widespread mischief in the land.” Narrated and classed as hasan by al-Tirmidhi, 1084. Classed as hasan by al-Albaani in Irwa’ al-Ghaleel, 1868). 

Both the verse and the hadeeth quoted point clearly to two things: 

1 – The command to arrange the marriage is addressed to the wali, which indicates that the matter has to do with him and the nikaah cannot be done unless he is involved in giving his female relative or ward in marriage to the one who has proposed marriage. The ahaadeeth that we have quoted clearly indicate this and support it. 

2 – It is not permissible for a wali to mistreat his ward and deny her her right to marriage; that is a kind of mistreatment that leads to great fitnah that affects both religious commitment and worldly interests. 

If both the woman and her wali act in accordance with this, the security of the family will be achieved and a great deal of evil will be removed from matters of religion and morals. 

But if the wali refuses to give her her rights to marriage with no legitimate reason, it is permissible for her to move to another, more distantly-related, wali, such as her older brother, paternal uncle or grandfather, so long as that is done on the orders of the shar’i qaadi, and not by her or by her walis. If there is no wali from her family, it is permissible for the qaadi or someone who is in a similar position to act as her wali and arrange her marriage, because it is narrated that ‘Aa’ishah (may Allaah be pleased with her) said: The Prophet (peace and blessings of Allaah be upon him) said: “Any woman who gets married without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid, and if there is a dispute then the person in authority is the wali of the one who has no wali.”  

Based on this, there is no sin on a woman whose wali denies her her right to marriage if she refers the matter to the Muslim qaadi and appoints her grandfather, paternal uncle or older brother as her wali. 

Shaykh Saalih al-Fawzaan was asked about a similar issue and he replied: 

It is not permissible for a woman to arrange her own marriage. If she arranges her own marriage, then her marriage is invalid according to the majority of scholars, both ancient and contemporary. That is because Allaah, may He be exalted and glorified, addresses walis with regard to the issue of marriage and He says (interpretation of the meaning): 

“and (also marry) the Saalihoon (pious, fit and capable ones) of your (male) slaves”

[al-Noor 24:32]

And the Prophet (peace and blessings of Allaah be upon him) said: “If there comes to you one with whose religious commitment and character you are pleased, then marry (your daughter or female relative under your care) to him…” And he (peace and blessings of Allaah be upon him) said: “There is no marriage without a wali and two witnesses of good character.” 

With regard to what the questioner mentions about having read in some books of fiqh that a woman may arrange her own marriage, this is the weaker view, and the correct view is that which is supported by evidence that indicates the opposite.  

With regard to what she says about her situation and that her opinion goes against her father’s, because her father wants her to marry a man who is of good lineage and status and is compatible with her, whereas she does not think that is important, and rather she is inclined towards marrying a man who she thinks is religiously committed, even if he is not of good lineage and status or compatible with her, her father is in the right in this case, and her father is more far-sighted. She may imagine that this person is good for her when in fact he is not good for her, and she has no right to go against her father’s wishes so long as he is looking out for her best interests. If it happens that another person is good for her and is compatible with her in status, lineage and religious commitment, but her father refuses to give her to him in marriage, then in that case he is being unjust in preventing the marriage, and the role of wali then passes to the next closest guardian among her relatives. But in this case it is essential to refer the matter to the qaadi so that the guardianship may be passed from the unjust father to another wali. Neither she nor any of her other walis has the right to conduct her marriage without the approval of her father. It is essential to refer the matter to a Muslim qaadi who will examine the matter and assess the situation. If he thinks that the guardianship should pass to someone else, he will transfer it, according to what is best. It is essential for things to be done properly with regard to marriage. End quote.

Al-Muntaqa min Fataawa al-Shaykh al-Fawzaan, 5/242, 243 

Thirdly: 

Whoever gets married in a manner that is not Islamically acceptable, such as a woman who gets married without a wali, her marriage is invalid and the couple must be separated immediately. The children are to be attributed to the man who married the woman, if they thought that what they did was permissible, but if they knew that their marriage was invalid, then the children must be attributed only to their mother. 

This invalid marriage leads to many negative consequences, such as: loss of the woman’s rights, because there is no proof of this marriage, so her entitlement to the mahr is not proven, nor is she entitled to maintenance. It also leads to the spread of immorality and corruption in society, especially among students, since it is possible, by means of these false contracts, for every pregnant woman or every man and woman who are found in a dubious situation, to claim that they are married by means of customary marriage. It also means that it is not possible to prove the children’s lineage in such a marriage, which means that they and their lineage will be lost.  

The way to set this matter straight is to go to the wali and tell him frankly what has happened, then to do the marriage contract again, with his agreement. If he does not agree, then they should be separated. 

And Allaah knows best.