How can she be sure of the Islam of a person whom she wants to marry?

You need to know, may Allaah help you to adhere firmly to Islam, that it is not permissible for a Muslim to love a kaafir, because Allaah says (interpretation of the meaning): You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their kindred (people). [al-Mujaadilah 58:22]

As you say that you love him, you have to give up this love for the sake of Allaah; whoever gives up a thing for the sake of Allaah, Allaah will compensate him with something better.

If this young man declares his Islam and you fear that he is not sincere in his Islam, remember what Allaah said (interpretation of the meaning): O you who believe! When believing women come to you as emigrants, examine them; Allaah knows best as to their Faith, then if you ascertain that they are true believers send them not back to the disbelievers. They are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them. [al-Mumtahinah 60:10]

So he could be tested by asking him about Allaah, His religion, and His Prophet Muhammad (peace and blessings of Allaah be upon him), and about the religion that he claims to have left.

You could also make sure of his Islam by watching to see if he persists in the obligatory acts of worship, such as prayer especially if there is a mosque nearby and fasting.

If a person especially a new Muslim is really serious about Islam, this will also manifest itself in other ways, such as whether he bothers to ask questions about the rulings on halaal and haraam.

He will also be concerned about changing the way he is, such as ridding himself of kaafir rituals and giving up things that are munkar and haraam that he used to do before he was Muslim.

Whether he is truly Muslim will also be seen from the way he hates the kufr that he used to follow before. The Prophet (peace and blessings of Allaah be upon him) said: There are three things, whoever attains them will find the sweetness of faith: when Allaah and His Messenger are more beloved to him than anyone else; when he loves a person and loves him only for the sake of Allaah; and when he would hate to return to kufr after Allaah has saved him from it, as he would hate to be thrown into the fire. (Narrated by al-Bukhaari, 21).

We also want to be sure that there is no forbidden relationship, because a Muslim woman is not permitted to do this. She should not touch or be alone with a non-mahram man (one to whom she is not married or related by close blood ties). We ask Allaah to choose good for you and to decree it for you and to keep you safe from all evil. May Allaah bless our Prophet Muhammad.