Pidyon haBen is the ceremony by which the father redeems his first born son from the Cohen. The Pidyon takes place after 30 days from the day of birth. As we have explained, there are certain conditions that need to be met in order to perform the Pidyon ( see here).
If possible, one should arrange to have a Minyan for the Pidyon.
The parents dress themselves and their son as they would do for a holiday.
The father brings 5 sheqels of silver.
The Cohen asks the mother if her son is the bekhor. If the mother says "yes", the Cohen proceeds to recite a text (ze haben bekhor hu...) where he quotes the Mitzva of redeeming the first born and asserts that, indeed, the parents have expressed their will to redeem him (veabikha veimekha mebaqeshim lifdotekha...).
The Cohen then asks the parents: "Which would you rather have-your firstborn son, or the five coins which you are obligated to give me for the redemption of this your firstborn son?"
To which the father answers: "I want, my firstborn son, and here you have five coins which are required of me for the redemption".
Then the father says the blessings: ...'al pidyon haben. and ... shehecheyanu.... And he places in front of the Cohen the 5 shequels.
The Cohen takes the coins and says: "I've received the 5 silver coins for the redemption of your son. He is now redeemed according to the law of Moshe and Israel (kedat moshe veIsrael)". The Cohen blesses the child, placing his hands over his head. At the end of that blessing the Cohen also blesses the parents and wish them to merit to fulfill all the Mitzvot of the Tora.
The Cohen can keep for himself the 5 shequels, or give it back to the parents, if the Cohen wishes to do so.
Video of a Ceremony of Pidyon haBen in Manchester, England (Ashkenazi)