I am a Muslim which have had a relationship with a young Muslim woman, and she is embarrassed since one month. My parents as well as her would be ready to marry us if we respect the rules of Allah, within the process. I would like to know which are the steps to follow in order to get married according to the rules. Those Islam allow abortion if it has less than 40 days?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

You cannot marry this woman unless both of you make sincere repentance from the sin you committed.  Allah Says (interpretation of meaning): {The adulterer marries not but an adulteress or a Mushrikah and the adulteress none marries her except an adulterer or a Muskrik [and that means that the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely he is either an adulterer, or a Mushrik (polytheist, pagan or idolater, etc.) And the woman who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer, then she is either a prostitute or a Mushrikah (female polytheist, pagan, or idolatress, etc.)]. Such a thing is forbidden to the believers (of Islâmic Monotheism).}[24:3].

According to the correct opinion of Muslim scholars you may marry her while she is pregnant from Zina as long as she is pregnant from you.  This is the opinion of al-Shafi’eyah and al-Ahnaf.  After having completed the legal marriage contract you may cohabit with her since the sperm in her womb belongs to you. 

However, abortion is not allowed whether the fetus is less than forty days or more, except for some legal reason such as danger to the life of the mother or the like.

Do not try to correct your mistake by committing another mistake.  The way to make up for this sin is to make sincere repentance, and then marry her.