What is the proper way to do netilat yadayim after the bathroom?

One should preferably wash his hands until the wrist, or in a time of need at least until his knuckles (Mishna Berura 4: 38).

There is a discussion as to whether one should wash 3 times with a cup like netilat yadayim in the morning, or it suffices just to wash regularly. The halacha is like the latter, that is suffices just to wash regularly, although many people are stringent to wash 3 times with a cup (Mishna Berura ibid 39).