How To Make Up For Missed Fasts
Question

How should a Muslim make up for missed fasts?
Praise be to Allah.Not fasting for a reason
If you did not fast for a reason, such as sickness or travelling, or menstruation in the case of women, then you must make it up after Ramadan, and you must make up the number of days that you did not fast, because Allah 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.” [al-Baqarah 2:185]. 
‘Aishah (may Allah 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-Bukhari (321) and Muslim (335)
When to make up missed fasts 
The time for making up the fasts lasts until the next Ramadan begins; you can make them up at any time during this period, on consecutive days or separately . 
It is not permissible for one to delay making them up after the following Ramadan, unless he has an excuse. 
Not fasting with no excuse 
But if you did not fast deliberately, with no excuse, then one of two scenarios must apply: 

You decided not to fast from the night before, and you 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 Allah 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-Bukhari (2697) and Muslim (1718) 
You did intend to fast from the night before, and you started the day fasting, then you broke your fast during the day with no excuse. You have to make up for this day, because you started to do it, which makes it like a vow that you must fulfil. 

Hence the Prophet (peace and blessings of Allah be upon him) commanded the one who had intercourse during the day in Ramadan to make up that day, and he said to him: “Fast one day in its place.” (Narrated by Ibn Majah (1671), classed as sahih by al-Albani in Sahih Sunan Ibn Majah) 
Fidyah for missed fasts
In addition to that, if you broke the fast during the day without any excuse by having intercourse , you must make it up and also offer expiation. 
The one who breaks his fast with no excuse also has to repent to Allah, regret what he has done, resolve never to do it again, and do a lot of righteous deeds such as observing nafl fasts and so on. Allah 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).” [Ta-Ha 20:82]. 
For more, please see these answers: 34564 and 11141 .
And Allah knows best.