|take off her captive's garb|
To remove from her any taint of idolatry (Midrash Aggadah). Also to make her less attractive (Rashi; Rashbam; Ibn Ezra).
|a full month|
Actually, the man could not marry her for 90 days (Yevamoth 48b; Yad, Melakhim 8:5). He thus would have to wait an additional two months after her mourning period was over.
|her father and mother|
As well as their idolatrous religion, which she must abandon (Yevamoth 48b; Yad, Melakhim 8:5; Ramban). This is an act of mercy (Moreh Nevukhim 3:41). This delay also gives the girl a chance to accustom herself to Judaism and refrain from mentioning idolatrous deities (Midrash Aggadah). Thirty days is a normal mourning period; see Numbers 20:29.
After converting her to Judaism. She is given 12 months to make up her mind to convert, after which she is sent away (Yad, Melakhim 8:7). However, others maintain that she may be converted against her will (Ramban).
|making her your wife|
Some say through a regular marriage ceremony (Yad, Melakhim 8:6), while others maintain that she becomes his wife through intercourse alone (Ramban). In either case, she has the full rights of a wife, as in Exodus 21:10 (Sifri).