Say the niyat (intention) for wudu:
Arabic:
Transliteration: NA'WHYTU - UN - ATAWAZZA - LIS- SALATI- TAQAR- RUBAN - ILLUL - LAHI - TA'ALA
English: I intend to do the ritual ablution to perform the Salat (prayer) to enable me to be near to Allah Ta'ala.

Wash your hands 3 times

• Use left hand to wash right hand, up to and including the wrist, 3 times.
• Then, use right hand to wash left hand, up to and including the wrist, 3 times.

While washing your hands, say the following dua:
Arabic:
Transliteration: ALLAH - HUM - MAH - FIZNEE - YADAYYA - UN - IRTEKABIL - MA'ASI - WAL - MALA'HEE.
English: Oh Allah! keep my both hands safe from sins and bad work.

Rinse water in your mouth 3 times

• Cup right hand with water and put in mouth, then spit it out, 3 times.

While rinsing your mouth, say the following dua:
Arabic:
Transliteration: Allah humma Ani ala tilawatil qurani wa zikrika wa shukrika wa husne ibaadatika.
English:

Snuff water in nose 3 times

While cleaning your nose, say the following dua:
Arabic:
Transliteration: Allah humma arhanee rahatal janati.
English:

Wash face 3 times

While washing your face, say the following dua:
Arabic:
Transliteration: Allah humma tabyaz wajhee youmun tabyuzu wujuhoon ouliayak.
English:

Wash forearms 3 times

• Wipe right forearm with left hand, all the way up to and including the elbow, 3 times.
• Wipe left forearm with right hand, all the way up to and including the elbow, 3 times.

While washing your right arm, say the following dua:
Arabic:
Transliteration: Allah humma ateeni kitabi be ameani wa hasbinee hisabun yaseera.
English:

While washing your left arm, say the following dua:
Arabic:
Transliteration: Allah humma la tateeni kitabi be shimali wala minawara zahree.
English:

Wipe water over head/hair 1 times

• It has been recorded that the Prophet used to wipe his head three different ways:
  1. Wiping all of his head. 'Abdullah ibn Zaid reported that the Prophet  wiped his entire head with his hands. He started with the front of his head, then moved to the back, and then returned his hands to the front.
  2. Wiping over the turban only.
     • Said 'Amru ibn Umayyah, "I saw the Messenger of Allah  wipe over his turban and shoes." (Related by Ahmad, al-Bukhari and Ibn Majah) .
     • Bilal reported that the Prophet said, " Wipe over your shoes and head covering. " (Related by Ahmad.)
     • 'Umar once said, "May Allah not purify the one who does not consider wiping over the turban to be purifying." Many hadith have been related on this topic by al-Bukhari, Muslim and others. Most of the scholars agree with them.
  3. Wiping over the front portion of the scalp and the turban. Al-Mughirah ibn Shu'bah said that the Messenger of Allah, upon whom be peace, made ablution and wiped over the front portion of his scalp, his turban and his socks. (Related by Muslim.) There is, however, no strong hadith that he wiped over part of his head, even though al-Ma'idah: apparently implies it. It is also not sufficient just to wipe over locks of hair that proceed from the head or along the sides of the head.
• If you are a female and a non-mahram male (or non-Muslim who you believe may describe you to others) may see you (such as in a public bathroom, etc.), do not remove your hijab or niqab... keep it on and wipe over it.

While rinsing your mouth, say the following dua:
Arabic:
Transliteration: Allah humma azalnee tahti zilli arshika youmullah zilla ila zilli arshika.
English:

Wipe the inside and back of ears 1 time

• Wash both ears at the same time

While rinsing your mouth, say the following dua:
Arabic:
Transliteration: Allah humma azalnee minal lazeena sayastamiunal khoula fayatibee unal ehsanahu.
English:

Wipe the back of neck 1 time

Wash feet

• Wash right foot, including the ankle, with left hand, 3 times.
• Wipe between each toe on right foot, with left hand pinky, 1 time.
• Wash left foot, including the ankle, with right hand, 3 times.
• Wipe between each toe on left foot, with right hand pinky, 1 time.
  • Once the Prophet remained behind us in a journey. He joined us while we were performing ablution for the prayer which was over-due. We were just passing wet hands over our feet (and not washing them properly) so the Prophet addressed us in a loud voice and said twice or thrice: " Save your heels from the fire. "   [Bukhari 1:164, Narrated 'Abdullah bin 'Amr]
  • "...and then he washed his feet up to the ankles."   [Bukhari 1.186, narrated Amr]

While rinsing your mouth, say the following dua:
Arabic:
Transliteration: Allah humma subbit khadami alla siratal youma tazzalal ikhdam.
English:

Then say the following:
Arabic:
Transliteration: AA - UZU - BIL - LAHI - MINASH - SHAYTAAN - NIR - RAJEEM.
Translation: I seek refuge in Allah from the rejected Shaitaan (Devil).