Firstly: 

Through this website we will send a message to this non-Muslim woman and others, telling them that no one can attain true life, happiness and peace of mind unless he believes in Allaah as his Lord, Islam as his religion and Muhammad as his Prophet. For all of the universe is created, and its Creator is Allaah. He is the One Who raised the heavens with no pillars and spread out the earth, and created the mountains to stabilize it, and created the sea and the rivers. 

“Surely, His is the creation and commandment. Blessed is Allaah, the Lord of the ‘Aalameen (mankind, jinn and all that exists)!”

[al-A’raaf 7:54 – interpretation of the meaning]

Once this is clear, it should be understood that Allaah sent Messengers to His slaves, to show them the way, teach them and guide them to the path of salvation. 

“Messengers as bearers of good news as well as of warning in order that mankind should have no plea against Allaah after the (coming of) Messengers”

[al-Nisa’ 4:165]

And He ended the series of His Messengers with Muhammad (peace and blessings of Allaah be upon him): 

“Muhammad is not the father of any of your men, but he is the Messenger of Allaah and the last (end) of the Prophets”

[al-Ahzaab 33:40 – interpretation of the meaning]

Allaah sent him with the religion of Islam other than which He will not accept any religion from anyone: 

“And whoever seeks a religion other than Islam, it will never be accepted of him, and in the Hereafter he will be one of the losers”

[Aal ‘Imraan 3:85 – interpretation of the meaning]

Secondly: 

With regard to when and how she may become Muslim: 

It is very easy indeed. All she has to do is to say “Ashhadu an laa ilaaha illaaha ill-Allaah wa ashhadu anna Muhammad ‘abduhu was rasooluhu (I bear witness that there is no god except Allaah and I bear witness that Muhammad is His slave and Messenger).” Once she says that, she becomes Muslim. She should hasten to do that, because death may come suddenly, and no one knows whether he will live until tomorrow or not. 

We welcome her as our sister in Islam, and we ask Allaah to inspire her and guide her to do that which will bring her happiness in this world and in the Hereafter. 

Thirdly: 

What is stated in this question is that the woman is “non-Muslim”. This may be understood as meaning that she is one of the people of the Book – i.e., Jewish or Christian – or it may be understood as meaning that she is something else – such as Buddhist, Zoroastrian or communist. If the woman who wants to marry a Muslim man is one of the people of the Book, there is no shar’i impediment to this marriage, so long as it fulfils the shar’i conditions, such as the requirement that she be chaste. But the Muslim husband should be keen to bring his wife into Islam so as to save her from eternity in the Fire and so that he and his children will have a home that is based on Islam. 

But if the woman who wants to marry a Muslim man is not one of the people of the Book, then it is not permissible for a Muslim to marry her. 

Allaah says (interpretation of the meaning): 

“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress), even though she pleases you. And give not (your daughters) in marriage to Al‑Mushrikoon till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allaah invites (you) to Paradise and forgiveness by His Leave, and makes His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember”

[al-Baqarah 2:221]

Ibn Katheer said: 

Here Allaah forbids the believers to marry mushrik woman who worship idols, and if this were general in meaning, it would include every mushrik woman, whether she is of the people of the Book or is an idol worshipper, but the woman of the people of the Book are excluded from that in the verse (interpretation of the meaning): 

“(Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due Mahr (bridal-money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girlfriends”

[al-Maa'idah 5:5]

‘Ali ibn Abi Talhah said, narrating from Ibn ‘Abbaas concerning the words “And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone)”: Allaah excludes from that the women of the people of the Book. This was also the view of Mujahid, ‘Ikrimah, Sa’eed ibn Jubayr, Makhool, al-Hasan, al-Dahhaak, Zayd ibn Aslam, al-Rabee’ ibn Anas and others. And it was said that what is meant is the mushrikoon who worship idols, and it does not mean the people of the Book at all. This meaning is close to the first meaning. And Allaah knows best. 

Tafseer Ibn Katheer, 1/474 

Whilst noting that this is permissible, we should also remember that Islam encourages the Muslim man to marry a Muslim woman who is religiously committed, because the Muslim’s life with his wife is a complete and comprehensive life which involves chastity, lowering the gaze, and protecting and looking after the house and children. These and similar things cannot be achieved except with a religiously-committed wife. 

See the answer to question no. 12283; also the answer to question no 20227, which gives more details on the bad consequences of marriage to a non-Muslims woman. In the answer to question no. 3320 it states that it is not permissible to allow her to celebrate (non-Islamic) festivals inside or outside the home. 

And Allaah knows best.