Correct Procedure for Netillas Yadayim in the morning:
• One should wash with a cup. This is due to Rashba's opinion that we
are washing just as the kohen washed his hands with a utensil every
morning. (SA 4.7, Pri megadim MSZ 1.)
• You should wash your full hand up to your wrist. If you don't have
enough water, then you can wash until your knuckles (Mishna Berurah
4.9)
• One should pick up the cup with your right hand (even lefties),
transfer it to your left, and alternate pouring on both hands until
each hand is washed three times. (SA 4.2+10). Some have the minhag to
wash each hand an extra time (4) to wash away the impure water. (Gra)
• One should wash his mouth and face. (MB 4.2+9),
• one should raise his hands after she washes like someone who is
"accepting something" (MB 4.9)
• One should be particular not to walk four cubit feet before washing
his hands. Some give a limud zechus for people that aren't stringent
based on a tradition from the Gra that once the ger tzedek died, no
more impure spirit rests on the hands. Another reason people
aren't strict is that since it's only brought in Kabbalah, it's only
pious folk. Furthermore, it has been argued that a home is one domain.
Since the Mishna Berurah and most achronim are very particular about
it, one should try to wash near his bed. (MB 1.1, Shvus Yaakov 3.1,
Shulchan Haleivi 1.1, Halichas Shlomo)