The answer to this question is that there isn't a "specific way" as we have for wudhu or ghusl . The process of shaving can be done anyhow provided you exercise precaution in doing so.
As regards whether it is an obligation or optional, the jurists (may Allaah have mercy upon them) agreed that it is a recommended act for men and women, however, some jurists (may Allaah have mercy upon them) are of the view that it is an obligation on the woman if her husband orders her to do so.
Ibn Muflih (may Allaah have mercy upon him) said in Al-Aadaab
Ash-Shar'iyyah (the religious etiquettes): 'It is disliked to delay
shaving the pubic hair, plucking out armpit hair and trimming one's
moustache more than the stated period.' The stated period is forty
days as Imaam Muslim(may Allaah have mercy upon him) reported that
Anas (may Allaah be pleased with him) said: "The period that was
prescribed for us to trim our moustache, clip our nails, pluck out our
armpit hair and shave our pubic hair is forty days." Of course it
was the Prophet Sallallaahu `alayhi wa sallam ( may Allaah exalt his
mention ) who determined for them this period of forty days, so it is
disliked to leave them longer than this period of time.
I had asked some knowledgeable people in my local area and they have said that it should be done in 40 days as in the above hadith. Though some people claim that it nullifies all your good deeds if not shaved within 40 days, the shaving of hair doesn't come as a compulsion for making your prayer valid, rather it is an act of Fitrah as mentioned in the hadith in the question. They are part of 'Taharah' (Cleanliness)
Regarding Scissors, the main objective is to cut them short, so the use of scissors is deemed permissible.
It was said to Ahmad Bin Hanbal: What is your opinion of a man that
cuts down below with scissors and he does not cut it all off? He said:
I hope that is sufficient by the will of Allah. It was said: O Abu
Abdullah what do you say about a man who plucks his pubic hair? He
said: And does anyone have the strength to do this?. And shaving the
pubic hair, plucking it,removing it with lime or arsenic are all
permitted as long as the aim is fulfilled which is the removal of the
hair and cleaning the place.
But still it is better not to take chances by leaving them to grow because:
On the authority of Abu Muhammad al-Hasan bin Ali bin Abi Talib, the
grandson of the Messenger of Allah, sallallahu ëalayhi wasallam, and
who is dearest to him, radiyallahu ëanhuma, who said: ìI committed to
memory from the Messenger of Allah, sallallahu ëalayhi wasallam, (the
following words): Leave that about which you are in doubt for that about which you are in no doubt. [Al-Tirmidhi and al-Nasaíi related
it, and al-Tirmidhi said: It is a good and genuine Hadith]
So better not take risks. Allah knows best!!
Baarakallahu Feekum. :)