Praise be to Allah.
If the girl does not have a guardian, her marriage should be done by the sharee’ah judge. If there is no sharee’ah judge, then her marriage should be done by a man of status among the Muslims, such as the imam of the mosque or Islamic centre, or a well-known scholar. If none of these are available, then her marriage should be done by one of the Muslim men. See the answer to question number 48992.
In order for the marriage to be valid, it is essential that it be witnessed by two Muslim witnesses, who should testify that the proposal was made by the guardian and the acceptance by the husband, because the Prophet (blessings and peace of Allaah be upon him) said: “There is no marriage except with a guardian and two witnesses of good character.” Narrated by al-Bayhaqi from the hadeeth of ‘Imraan and ‘Aa’ishah; classed as saheeh by al-Albaani in Saheeh al-Jaami, no. 7557.
If you are in one city and the girl is in another city, and she does not have a guardian as you said, then the way to do the marriage is for her guardian to be one of the people of her city, such as the imam of the mosque or the Islamic centre, as stated above. He should make sure that she wants to get married and that she is pleased with you. Then he should appoint a person to act as his deputy in your city, who can do the marriage contract with you; or the marriage contract can be done between you and him by phone or by a chat program on the Internet, in the presence of witnesses with you or with him who can hear his proposal and your acceptance.
The correct view is that a marriage done over the phone is permissible when there is certainty that it is free of any deceit.
We put the following question to Shaykh Ibn Baaz (may Allaah be pleased with him):
I want to do the marriage contract with a girl but her father is in another city, and at present I cannot travel to him in order for us to meet and do the marriage contract, due to financial and other reasons. I am in a foreign country. Is it permissible for me to contact her father and for him to say to me, “I give my daughter so-and-so to you in marriage” and for me to say “I accept”, and the girl is willing, and there are two Muslim witnesses who can hear my words and his words via loudspeaker on the phone? Is this regarded as a legitimate shar’i marriage contract? He replied that what is mentioned, if it is genuine (and there is no deceit involved), fulfils the conditions of the shar’i marriage contract and the contract is valid.
And Allaah knows best.