Allah made it obligatory upon every Muslim to fast the month of Ramadan. Allah, ta^ala, said in the Qur’an:

يَا أَيُّهَا الَّذِينَ آمَنُواْ كُتِبَ عَلَيْكُمُ الصِّيَامُ

Ya ayyuha-lladhina amanu kutiba ^alaykumus–siyam.

Ayah 183 of Suratul-Baqarah means: {He (Allah) made fasting obligatory upon you.}

Fasting the month of Ramadan was made obligatory during the month of Sha^ban in the second year after the immigration.

Fasting the month of Ramadan is a great obligation and among the most important matters of Islam.
The Muslims look forward to this month because it is the month of
goodness, obedience, and blessings. It is also the best month of the
year, and in it is the best night of the year, that is, the Night of Qadr.

Fasting
is abstaining from anything that invalidates the fast during the day,
along with having made the intention during the night. It is an
obligation upon every pubescent, sane, and able Muslim to fast.
However, it is not valid from the menstruating and postpartum-bleeding
women.

Fasting Ramadan becomes obligatory by one of two things:

Finishing thirty (30) days of Sha^ban.

Seeing the crescent of Ramadan on the thirtieth night of Sha^ban. This is due to the saying of the Prophet, sallallahu ^alayhi wa sallam:

صوموا لرؤيته، وأفطروا لرؤيته، فإن غم عليكم فأكملوا عدة شعبان ثلاثين يوما

Sumu liru’yatihi wa aftiru liru’yatih(i). Fa’in ghumma ^alaykum, fa’akmilu ^iddata Sha^bana thalathina yawma.

Which
means: “Fast upon seeing the crescent and break your fast upon seeing
it. If you could not see the crescent because it was cloudy, then
finish the whole thirty days of Sha^ban.” (Related by al-Bukhariyy and Muslim.)

The
one who sees the crescent has to fast. Moreover, the one who does not
see it, but is informed by a upright, trustworthy, free Muslim who does
not lie is also obligated to fast.

Fasting has two integrals:

The
intention in the heart every day. One intends in his heart, for
example: “I intend to fast tomorrow to fulfill the obligation of
fasting Ramadan this year, faithfully and seeking the reward from Allah.”

The time of the intention is from sunset until the Fajr prayer begins.

To abstain from anything that invalidates fasting, from the appearance of the true dawn to the sunset.

Note:

It is unlawful (haram) to fast the two days of ^Idul-Fitr and ^Idul-Ad–ha, and the three days after ^Idul Ad–ha, known as the days of Tashriq.