Praise be to Allah.
If a man has decided to propose to a woman, it is permissible for him to look at that which may encourage him to marry her, because of the report narrated by Abu Dawood (2082) from Jaabir ibn ‘Abd-Allaah who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “When one of you proposes to a woman, if he can look at that which may encourage him to go ahead and marry her, let him do so.” He said: I proposed to a girl and I used to hide myself from her until I saw that which encouraged me to marry her, and I went ahead and married her. This hadeeth was classed as saheeh by al-Albaani in Saheeh Abi Dawood.
For more information on the guidelines on looking, see the answer to question no. 2572.
If you cannot travel to see the one to whom you want to propose, then you can look at a picture of her, but you should realize that a picture is not a true reflection of reality. A woman may appear more beautiful in a picture than she really is, and vice versa.
You also have to get rid of this picture and not keep it, and you have to be careful so that no one else sees it but you.
Do not ask for a picture until you have feel that you want to marry her, after asking about her religious commitment and situation, and you think that you will most likely be accepted. When there is nothing left to be done but seeing her, then ask for the picture at that point, because of the report narrated by Ahmad (18005) and Ibn Majaah (1864) from Muhammad ibn Maslamah, who said: I proposed marriage to a woman, then I hid and waited to see her until I saw her among some date palm trees that belonged to her. It was said to him: Do you do such a thing when you are a companion of the Messenger of Allaah (peace and blessings of Allaah be upon him)? He said, “When Allaah causes a man to propose to a woman, there is nothing wrong with him looking at her.” It was classed as saheeh by al-Albaani in Saheeh Ibn Majaah.
Al-Nawawi (may Allaah have mercy on him) said: If he wants to propose to her it is mustahabb for him to look at her lest he come to regret it. Another view is that this looking is not mustahabb, rather it is permissible, but the former view is the one that is correct, because of the ahaadeeth. It is permissible to look repeatedly in order to have a good idea about her physical appearance, whether the looking is with her permission or not. If it is not easy to look, he may send a woman to look at her and describe her to him. End quote from Rawdat al-Taalibeen (7/19).
Looking at one’s fiancée or at her picture is subject to the condition that there be no provocation of desire, so he should look at her without pleasure.
It says in Mataalib Ooli al-Nuha (5/12): If the one who proposes to a woman is certain that there will be no provocation of desire when looking at her, without being alone with her, he may look at her. If he is alone with her or there is the fear that desire may be provoked, then it is not permissible. End quote.
And Allaah knows best.