Immediately after the father recites the two Berachot over the Pidyon Haben – "Asher Kideshanu…Al Pidyon Haben," and "Shehehiyanu" – he hands the money to the Kohen. The father must ensure not to hand the money to the Kohen before or during the recitation of the Beracha, because the Beracha over a Misva must be recited in full before the performance of the Misva.
When the father gives the money to the Kohen, he should make a declaration announcing that he gives the money for the sake of Pidyon Haben ("Zeh Pidyon Beni Bechori"). The Kohen receives the money and makes a declaration acknowledging that the money was received for the sake of the child’s redemption, and the child is thus redeemed in accordance with Torah law (listen to audio recording for precise text of the declaration). After making this declaration, the Kohen places the money on the child’s head and says, "Zeh Tahat Bincha" ("This is in place of your son"). Our custom is that the Kohen then places his hand on the child’s head and says, "Hashem Yishmerecha Vi’yehayeka" ("God shall protect you and keep you alive"), followed by Birkat Kohanim. The Kohen then recites a brief prayer that just as the boy was privileged to have a Pidyon Haben, he should also be privileged to learn Torah, perform Misvot, and stand under a Hupa (listen to audio recording for precise text of the prayer).
It is customary after the Pidyon Haben to recite "Boreh Peri Ha’gefen" over a cup of wine, and then recite the Beracha of Besamim over Hadasim. The custom to recite a Beracha over Hadasim at a Pidyon Haben appears in several sources, including the Rashba, Rabbenu Hananel (commentary to the Torah, Parashat Shofetim), the Meiri and the Sefer Ha’hinuch. A Beracha is made over a cup of wine for the purpose of publicizing the Misva, but it is not entirely clear, at first glance, why Hadasim are used at the Pidyon Haben. Hadasim are used at a Berit Mila because of the concern that people may faint upon viewing the circumcision, and the fragrant smell of the Hadasim helps prevent fainting. At a Pidyon Haben, of course, there is no such concern. Some scholars therefore explained that the Hadasim are used to demonstrate that the cup of wine was drunk for the purpose of the Misva. Since wine is often drunk at meals, it would not be evident that the wine at the Pidyon Haben is special, and serves to publicize the Misva. Therefore, we include Hadasim to show that the wine is used for the Misva. Of course, the Hadasim are not indispensable to the Misva, and the obligation is fulfilled even without them.
Some people have the custom to recite a special Beracha after the Pidyon Haben, which is printed in some Siddurim ("Baruch Ata…Asher Kidash Ubar Bi’m’eh Imo…"; listen to audio recording for precise text). Those who recite this Beracha should ensure to do so without Shem U’malchut (meaning, without the phrase "Hashem Elokenu Melech Ha’olam").
Summary: At a Pidyon Haben, the father should give the money to the Kohen immediately after reciting the Berachot, but not before completing the Berachot. The father and the Kohen make declarations acknowledging the Pidyon Haben, as printed in Siddurim. It is customary after the Pidyon Haben to place the money on the infant’s head and then for the Kohen to place his hand on the infant’s head and recite Birkat Kohanim and a special prayer for the child. It is also customary after the Pidyon Haben to recite "Boreh Peri Ha’gefen" over a cup of wine and the Beracha of "Besamim" over Hadasim.