He masturbated a great deal during Ramadaan – what should he do?

The correct scholarly
view is that masturbation is haraam. For more information please see the
answer to question no.
329. 

With regard to the rulings concerning the daytime in
Ramadaan, please see the answer to question no.
38074. 

Young men have to fear Allaah their Lord, and keep away from
listening to or looking at the things that will provoke their desire. They
should make the most of Ramadaan to discipline themselves, for this is the
month of the Qur’an and the month of piety. It is not befitting for a Muslim
to fail to make the most of this month to forsake forbidden desires and seek
reward, fearing his Lord. Allaah says of the fasting person in a hadeeth
qudsi: “He forsakes his food, his drink and his desires for My sake.”
Narrated by al-Bukhaari, 1894; Muslim, 1151. 

Shaykh Ibn ‘Uthaymeen said: 

One should be patient in avoiding masturbation, because it is
haraam as Allaah says (interpretation of the meaning): 

“And those who guard their chastity (i.e. private parts,
from illegal sexual acts)

6. Except from their wives or (the slaves) that their
right hands possess,
for then, they are free from blame;

7. But whoever seeks beyond that, then those are the
transgressors” 

[al-Mu’minoon 23:5-7]

And the Prophet (peace and blessings of Allaah be upon
him) said: “O young men, whoever among you can afford to get married, let
him do so, for it is more effective in lowering the gaze and guarding one’s
chastity. And whoever cannot afford that should fast.” 

If masturbation were permissible, the Prophet (peace and
blessings of Allaah be upon him) would have told them to do it, because it
is easier and because people find pleasure in it, unlike fasting which is
difficult. Because the Prophet (peace and blessings of Allaah be upon
him) enjoined fasting instead, this indicates that masturbation is not
permissible. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen,
19.189. 

You should try hard to
get married so that you can give up this bad habit. Seek the help of your
Lord by praying to Him and obeying Him, so that you can rid yourself of this
sinful habit. 

We ask Allaah to purify your heart and protect you from sin,
and to help you to do that which He loves and which pleases Him. 

And Allaah knows best.