Praise be to Allah.
If he did not fast for a reason, such as sickness or travelling, or menstruation in the case of women, then he must make it up after Ramadaan, and he must make up the number of days that he did not fast, because Allaah says (interpretation of the meaning):
“and whoever is ill or on a journey, the same number [of days which one did not observe Sawm (fasts) must be made up] from other days”
‘Aa’ishah (may Allaah be pleased with her) said: That (i.e., menstruation) would happen to us and we would be told to make up the fasts, but we were not told to make up the prayers. Narrated by al-Bukhaari (321) and Muslim (335).
The time for making up the fasts lasts until the next Ramadaan begins; he can make them up at any time during this period, on consecutive days or separately.
It is not permissible for him to delay making them up after the following Ramadaan, unless he has an excuse.
See the answer to question no. 26865.
But if he did not fast deliberately, with no excuse, then one of two scenarios must apply:
1 – He did not decide not to fast from the night before, and he did not intend to fast. In this case making up the fast is not valid, because fasting is an act of worship that is linked to a specific time, and if a person fails to do it, it is not valid after that time, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever does an action that is not in accordance with this matter of ours will have it rejected. Narrated by al-Bukhaari (2697) and Muslim (1718).
2 – He did intend to fast from the night before, and he started the day fasting, then he broke his fast during the day with no excuse. He has to make up this day, because he started to do it, which makes it like a vow that he must fulfil. Hence the Prophet (peace and blessings of Allaah be upon him) commanded the one who had intercourse during the day in Ramadaan to make up that day, and he said to him: “Fast one day in its place.” Narrated by Ibn Majaah (1671), classed as saheeh by al-Albaani in Saheeh Sunan Ibn Majaah.
In addition to that, if he broke the fast during the day without any excuse by having intercourse, he must make it up and also offer expiation. For information on this expiation and the rulings thereon, please see the answer to question no. 49614.
The one who breaks his fast with no excuse also has to repent to Allaah, regret what he has done, resolve never to do it again, and do a lot of righteous deeds such as observing naafil fasts and so on. Allaah says (interpretation of the meaning):
“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)”
And Allaah knows best.