Praise be to Allah.

The correct procedure for wudoo is: a person should pour water from the vessel onto his hands three times, then put his right hand into the vessel and rinse his mouth and nose three times, then wash his face three times, then wash his arm up to the elbow three times, then wipe his head and ears once, then wash his feet up to the ankles three times. If he washes everything twice, or once, this is sufficient. Then after doing wudoo he should say: Ashhadu an laa ilaaha illa-Allaah wahdahu laa shareeka lah, wa ash-hadu anna Muhammadan abduhu wa rasooluh. Allaahumma-jalni min al-tawwaabeen wajalni min al-mutatahhireen (I bear witness that there is no god but Allaah Alone, with no partner or associate, and I bear witness that Muhammad is His slave and Messenger. O Allaah, make me one of those who repent and make me one of those who are purify themselves).

Fataawa al-Lajnah al-Daaimah, 5/231.

Before doing wudoo, one should say Bismillah, because of the hadeeth: There is no wudoo for the one who does not mention the name of Allaah when he starts. (Sunan al-Tirmidhi, 56)