The Five Obligatory Prayers and How to determine their due times

The five prayers are among the best acts of worship that the Muslim performs. Performing them is the best deed after having the correct belief in God and His Messenger. Prophet Muhammad, may Allah raise his rank, was asked what the best deed was and he said it was performing the obligatory prayers at the beginning of their times (al¬-Bayhaqiyy)
When we say “prayers” we are referring to an act of worshipping God which has a specific format as God revealed to Prophet Muhammad, may Allah raise his rank. The prophets from Prophet Adam to Prophet Muhammad, may Allah raise their rank, ordered their followers to pray as per God’s orders.
Since the prayer is the most important matter of Islam after having the correct belief in God and His Messenger, one must plan his life around the prayer. It would be a great sin to neglect praying when at work if a prayer was required at that time. If a believer is shopping at the mall or waiting at the airport and there is no way to get home or to a mosque, he is still obligated to perform the prayer within its due time instead of purposely leaving out or delaying the prayer. This indicates the importance of the obligatory prayer.
Doing the obligatory prayer on time takes priority over other non-obligatory matters. 

Verse 238 of Surat al-Baqarah means: “Perform the [five obligatory] prayers”.
The Messenger of Allah peace be upon him said what means:

“There are five prayers that Allah obligated the slaves to perform. Whoever performs them properly without belittling their obligation, Allah promised to admit him into Paradise. Whoever leaves them out does not have a promise from Allah to have Paradise without torture before. If He willed, He tortures him, and if He willed, He forgives him”. Narrated by Ahmad in his Musnad.

It is obligatory to perform each of these five prayers in its due time. It is better to perform each prayer early in its time.

Dhuhr (Noon) Prayer [Four rak^ahs (cycles)]:

Its time begins when the sun has declined westward from the middle of the sky (zenith). The time remains until the length of the shadow of an object becomes equal to that of the object per Se, in addition to the length of the shadow of that object when the sun was at its zenith. For example, if the length of your shadow when the sun is at its zenith is 5 feet and you are 6 feet high, then once your shadow becomes 11 feet long the Dhuhr prayer time ends.

^Asr (Mid-afternoon) Prayer [Four rak^ahs]

As soon as the Dhuhr prayer time ends the ^Asr prayer time starts. Its time remains until sunset.

Maghrib (Sunset) Prayer [Three rak^ahs]

After the entire disk of the sun has set, then the Maghrib prayer time begins. This prayer time lasts until the redness has disappeared in the western horizon.

^Isha’ (Nightfall) Prayer [Four rak^ahs]

As soon as the Maghrib prayer time is finished the ^isha’ prayer time begins. You can be certain that this prayer time is in when you can see many small stars in the sky on a clear night. This prayer time lasts until the true dawn appears.

Subh or Fajr (Dawn) Prayer [Two rak ^ahs]

The true dawn begins when we see light spread at the horizon in the East. When the true dawn appears the Fajr prayer time has begun and this prayer time remains until the first glimpse of the disk of the sun appears on the Eastern horizon.