The Halachot of eating meat after dairy are different from the waiting required between eating dairy after meat. Three actions are required to insure that no residue of dairy remains when eating the meat. First, "Netilat Yadayim"-one must wash his hands to remove any remaining dairy residue. This does not mean the Netilat Yadayim performed with a cup, but washing the hands. Second, "Kinuah"-eating Pareve food to cleans the mouth of remaining dairy. Finally, "Hadaha"- drinking a liquid to wash one’s mouth out. After theses three preparations, it is permitted to eat meat.
Similarly, the Halacha prohibits eating fish and meat together. This is relevant to Shabbat when fish is served before the meat. The same process is required before eating the meat. One must first wash his hands, eat some bread and take a drink before continuing to eat the meat.
The same Halacha applies to those who follow the Ben Ish Hai and Hacham Ovadia and do not eat fish and dairy together. They must also perform these three preparations before eating fish after dairy or vice versa.
The Poskim discuss whether Netilat Yadayim is required in cases when the first dish was eaten with a fork, without contact to the hands. The Kaf HaHayim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939) was strict and rules that nevertheless, one should wash his hands. His reasoning may be because of "Lo Plug Rabanan"-the Rabbis instituted the Halacha without exception. Moreover, even if one eats with a fork, it could quite possibly occur that he touches the food with his fingers. This is the Halacha. However, there is room to be lenient and forgo Netilat Yadayim after drinking milk from a glass where, it is certainly not likely that one touches the liquid in the glass.
In order to eat meat after dairy, one must wash his hands, eat and drink something to prevent residual dairy from coming in contact with the meat. The same applies to eating meat and fish, as well as dairy and fish.