Firstly: The Ruling of Shaving and Cutting the Hair
Shaving the head or cutting the hair is one of the wajib acts of Hajj and `umrah. This is the position of the majority: the Hanafis, Malikis, and Hanbalis.
Secondly: Cutting the Hair Suffices One from Having to Shave
Cutting the hair suffices in place of shaving the head. Consensus on this was related by Ibn al-Mundhir, al-Nawawi, and Ibn Hajar.  However, there are many times when shaving is required according to some Malikis, such as when the hair is very short and when a man has matted his hair.
Thirdly: The Amount that must be Cut or Shaven
It is wajib to shave  Shaving is done with a blade, not with a machine, even if it is at the lowest setting, as that is not considered shaving, but shortening the hair. the entire head or cut all of the hair. This is the position of the Maliki and Hanbali schools. This is the chosen position of Ibn Baz and Ibn `Uthaymin.
Fourthly: The Superiority of Shaving to Shortening the Hair
Shaving the entire head is superior to shortening the hair.  Ibn Hajar says: “We can conclude from this that shaving is superior to cutting the hair. The reason is that it is more pronounced in terms of worship, more manifest in terms of submissiveness and humility, and more indicative of a sincere intention. One who cuts his hair maintains something that beautifies him. This is as opposed to one who shaves, for he feels that he has abandoned that for Allah the Exalted. It is also a sign of divestment.” (Fath al-Bari, 3/564) Consensus on this was related by Ibn `Abd al-Barr and al-Nawawi.
Fifthly: Women Shaving their Heads
Cutting the hair is legislated for women, not shaving.  The majority of jurists hold that she should shorten her hair by the amount of a fingertip. Ibn `Uthaymin says: “The view that is popular amongst women that a fingertip is measured by curling her hair over her finger until the two sides meet – that being the extent of what is wajib to cut – is false.” (Al-Sharh al-Mumti`, 7/329) Consensus on this was related by Ibn al-Mundhir, Ibn `Abd al-Barr, Ibn Qudamah, and al-Nawawi.
Sixthly: Passing a Blade over the Head of Someone with No Hair
Scholars have different regarding the case of someone with no hair, such as a bald man or one with sores on his head. The two strongest positions are:
The first position: It is mustahabb that he pass a blade over his scalp. This is the position of the Shafi`i and Hanbali schools, one position amongst Hanafis, and the position of a group of the Salaf.
The second position: It is not mustahabb that he pass a blade over his scalp. This is related from Abu Bakr ibn Dawud. It is the position of Ibn al-Qayyim, and al-Mirdawi was partial to it. This is the chosen position of Ibn `Uthaymin.
Seventhly: Starting with the Right Side of the Head
It is mustahabb to start with the right side of the head, meaning the right side of the one having their hair cut or shaved. One starts with the right side of the head then the left side. This is the position of the majority: the Malikis, Shafi`is, and Hanbalis. This is the chosen position of Ibn al-Humam of the Hanafi school.