How can I approach someone who I want to marry?

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.

If you mean by approaching her, to know her character/conduct, her religion and her beauty, this can be done through your mother, sister or one of your female relatives, or through a friend’s wife, or to sit with her in the presence of one of her Mahrams (male relative). Afterwards you may approach her guardian to say that you wish to marry her on the book of Allah and the Sunnah of the Prophet (Sallallahu Alaihi wa Sallam).  Apart from this, it is only following one’s desires and falling into undesirable consequences. 

Allah knows best.