Wuḍoo' (Ablution)
Adhān (The Call To Prayer)
Iqāmah
The Second Rak'ah (Unit Of Prayer)
The Middle Tashahhud (Testification Of Faith)
The Third And Fourth Rak'ah (Units Of Prayer)
The Final Tashahhud (Testification Of Faith)
Remembrance Of Allah After Praying
Witr Prayer
Jumu'ah (Friday Congregation)
Taraweeḥ Prayer (Optional Night Prayers During Ramaḍaan)
'Eid Prayer
Prayer For Seeking Guidance
Janāzah (Funeral Prayer)
Adhān

The adhaan is the call to prayer in Islam. It is performed five times a day from the mosque, and it serves as a reminder and a call to bring people to the prayer that is due.

The adhaan is called in the following way:

اللهُ أَكْبَرُ اللهُ أَكْبَرُ
اللهُ أَكْبَرُ اللهُ أَكْبَرُ
أَشْهَدُ أَنْ لَّا إِلَهَ إِلَّا اللهُ 
أَشْهَدُ أَنْ لَّا إِلَهَ إِلَّا اللهُ 
أَشْهَدُ أَنَّ مُحَمَّدًا رَّسُولُ اللهِ
أَشْهَدُ أَنَّ مُحَمَّدًا رَّسُولُ اللهِ
حَيَّ عَلَى الصَّلَاةِ  حَيَّ عَلَى الصَّلَاةِ
حَيَّ عَلَى الْفَلَاحِ حَيَّ عَلَى الْفَلَاحِ
* الصَّلاةُ خَيْرٌ مِّنَ النَّوْمِ الصَّلاةُ خَيْرٌ مِّنَ النَّوْمِ
اللهُ أَكْبَرُ اللهُ أَكْبَرُ
لَا إِلَهَ إِلَّا اللهُ 

Transliteration:

allaahu akbar, allaahu akbar
allaahu akbar, allaahu akbar
ash-hadu an-laa ilaaha ill-allah ash-hadu an-laa ilaaha ill-allah
ash-hadu anna muḥammadar-rasoolullaah ash-hadu anna muḥammadar-rasoolullaah
Ḥayya 'alaṣ-Ṣalaah, Ḥayya 'alaṣ-Ṣalaah
Ḥayya 'alal Falāḥ, Ḥayya 'alal Falāḥ
* aṣ-ṣalaatu khayrun minan-nawm, aṣ-ṣalaatu khayrun minan-nawm
allaahu akbar, allaahu akbar
laa ilaaha ill-allaah 

Translation:

Allah is the greatest, Allah is the greatest
Allah is the greatest, Allah is the greatest
I bear witness that none has the right to be worshipped except Allah, I bear witness that none has the right to be worshipped except Allah
I bear witness that Muhammad is the Messenger of Allah, I bear witness that Muhammad is the Messenger of Allah
Come to Prayer, Come to Prayer
Come to Success, Come to Success
* The prayer is better than the sleep, The prayer is better than the sleep (during fajr athan)
Allah is the greatest, Allah is the greatest
None has the right to be worshipped except Allah 

*The lines with the asterix are only included during the Fajr (Dawn) Prayer, this is due to the following narration:

'Abdullāh ibn Zayd (may Allah be pleased with him) narrated a dream in which he saw a man holding a bell in his hand:

"I said to him, 'O servant of Allah! Would you sell me this bell?' He replied, 'What do you want to do with it?' I said, 'To call the people to prayer' He said, 'Shall I not inform you what is better than that?' I said, 'Indeed' He said, 'Say: allaahu akbar, allaahu akbar, allaahu akbar, allaahu akbar (Allah is most great, four times), ash-hadu an-laa ilaaha ill-allah ash-hadu an-laa ilaaha ill-allah (I testify that there is no god but Allah, twice), ash-hadu anna muḥammadar-rasoolullaah ash-hadu anna muḥammadar-rasoolullaah (I testify that Muhammad is the Messenger of Allah, twice), Ḥayya 'alaṣ-Ṣalaah, Ḥayya 'alaṣ-Ṣalaah (come to prayer, come to prayer); Ḥayya 'alal Falāḥ, Ḥayya 'alal Falāḥ (come to success, come to success),  allaahu akbar, allaahu akbar (Allah is most great, twice); laa ilaaha ill-allaah (there is no god but Allah)...The Prophet (may the peace and blessings of Allah be upon him) said, 'Indeed, it is a true dream, God willing."  [Abū Dāwood 499]

And in the narration of Abū Maḥdhoorah:

"...If it is the morning prayer, you must pronounce; aṣ-ṣalaatu khayrun minan-nawm, aṣ-ṣalaatu khayrun minan-nawm, aṣ-ṣalaatu khayrun minan-nawm (prayer is better than sleep, twice)..."  [Abū Dāwood 500]

Ettiquettes of Adhaan

1. Placing the index fingers in the Ears

Abu Juhayfah (may Allah be pleased with him) narrated that:
"I saw Bilaal calling the Adhaan, and turning, and his (face) was following here and there, and his (index) fingers were in his ears..." [at-Tirmidhī: 197]

2. Standing and facing the Qibla (Direction of Makkah)

Muaadh ibn Jabal (May Allah be pleased with him) narrated:
"...And he turned his face towards the qiblah and said: Allah is most great, Allah is most great; I testify that there is no god but Allah, I testify that there is no god but Allah;..." [Abū Dāwood: 507

3. Being in the state of Wuḍū

Although this is not an explicit requirement, it is generally understood that someone who wants to remember or praise Allah, should try to be in a state of purity, since the adhaan is a form of remembrance and praise, this has been understood by many scholars from the following narration:

Al-Muhaajir ibn Qunfudh (may Allah be pleased with him) narrated that:

"...He came to the Prophet (may the peace and blessings of Allah be upon him) while he was relieving himself, and greeted him [with salām]. The Prophet (may the peace and blessings of Allah be upon him) did not return the greeting to him until he performed ablution. He then apologised to him, saying: 'I disliked remembering Allah except in the state of purification.'" [Abū Dāwood: 17]

If you can hear the Adhaan being called then you should recite the following supplication during it: 

http://duas.com/dua/166/dua-while-hearing-the-adhaan

And you should recite the following supplications after it:

http://duas.com/dua/167/dua-after-the-adhaan-1

http://duas.com/dua/168/dua-after-the-adhaan-2

http://duas.com/dua/169/dua-after-the-adhaan-3