Making up Missed PrayersAllaah says: “Verily, the prayer is prescribed for the believers at set times.” [Surah An-Nisaa: 103]
Imaam Mujaahid said: “This means that they are scheduled at obligatory times, which Allaah has set for them.”
The Prophet (sallAllaahu ‘alayhi wa sallam) said: “Whoever sleeps over (the time of) prayer or forgets it, should pray it when he remembers. There is no expiation for him except this.” 
This is the state of someone who has missed a prayer or several prayers due to some reason that is beyond his control. Allaah says: “Allaah does not burden a soul with more than it could bear.” [Surah Al-Baqarah: 286]
And the Prophet (sallAllaahu ‘alayhi wa sallam) said: “There is no neglect in sleep. Neglect is only found in one who doesn’t pray until the time for the next prayer comes in.” 
So if this is the state of someone, he should perform the prayer he missed immediately before the reason for which he missed it expires, such as waking up after sleeping or remembering after having forgotten…and so on and so forth. He should also perform the prayers he missed in sequential order according to their time-frames – the first one first, then the next one and so on.
“As for the one who deliberately leaves off praying without any (valid) excuse, whether due to disregard or laziness, to the point that the time for the prayer has passed, it is NOT VALID for him to make it up nor is the burden of responsibility uplifted from him. This is due to the fact that there is no valid proof which indicates that he is mandated to make it up or restore it or that one’s duty is fulfilled by making it up after its time has passed.” 
So if this is someone’s condition, he should perform as many voluntary and supererogatory prayers as he can without specifying a particular time for doing them since the Prophet (sallAllaahu ‘alayhi wa sallam) said: “Verily, the first thing that people will be held accountable for on the Day of Judgement from actions is the prayer. Our Lord will say to His Angels, even though He knows best: ‘Look into the prayer of My servant. Is it complete or deficient?’ If it is complete, it will be recorded for him as being complete. But if it is deficient in any way, He will say: ‘See if My servant has any voluntary prayers?’ So if he has voluntary prayers to his credit, He will say: ‘Compensate My servant’s obligatory (prayers) with the voluntary ones. Then his actions will be judged based on that.” 
Some people follow each obligatory prayer by performing a prayer that they missed. For example, they pray Dhuhr and then afterward, another Dhuhr that they missed previously, and the same with ‘Asr. This has no basis in the noble Sunnah, nor is there any valid proof known for it at all.
This is similar to what some people do like recording the number of prayers that they missed throughout the past years (!!), then performing them while subtracting the number they pray from the total. This is also from the newly-invented matters.
Footnotes: Reported by Al-Bukhaaree (597) and Muslim (684) from Anas bin Maalik
 Reported by Muslim (681) from Abu Qataadah
 Refer to “an-Nusoos ash-Shar’eeyah ath-Thaabitah fee Hukmi Qadaa-is-Salawaat-il-Faa’itah” (pg. 172) of Shaikh Muhammad Naseeb Ar-Rifaa’ee, may Allaah have mercy on him and forgive him.
 Reported by Abu Dawood (864), At-Tirmidhee (413), An-Nasaa’ee (1/232) and Ahmad (4/103), and it is an authentic hadeeth based on supporting narrations.
Also see http://www.islamqa.com/en/ref/111783