As most people are aware, it is forbidden to eat fish together with meat or chicken, because, as the Gemara comments, this could pose a medical risk. Few people, however, are aware of the procedure that is required after one eats fish and then wishes to eat meat or chicken. First, one must wash his hands, and according to Hacham Ovadia Yosef, this requirement applies even if one ate with a fork and knife and did not touch any fish. One does not have to wash the formal Netilat Yadayim as is required before eating bread, as this washing is required for cleanliness purposes, to ensure the removal of all fish residue. Secondly, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) rules (Parashat Pinhas, Shana Sheniya, 8) that one must wash the outside of his mouth after eating fish before eating chicken or meat. Additionally, one must rinse the inside of his mouth such as by gargling some water and according to the Ben Ish Hai, one should also drink something to ensure that the fish and meat do not mix in his stomach. Finally, one must eat something in between the fish and the meat. These Halachot are presented in Yalkut Yosef Berachot (vol. 2, p. 23; listen to audio recording for precise citation).
Many people customarily eat fish as an appetizer at the Shabbat meal, but, unfortunately, they are not aware of this procedure which must be followed afterward before proceeding to eat meat. It is therefore important to review these Halachot and ensure to perform the necessary measures before eating chicken or meat after the fish course.
Summary: After one eats fish, he should not eat meat until he does the following: washes his hands, washes the outside and inside of his mouth, eats something and drinks something.