Dedication to a deity is a very personal and serious rite. Oaths are taken very seriously in pretty much all paths, and it’s specific to the relationship between the deity and the devotee-to-be. Such vows should be carefully worded and thought over, as they can easily become a burden rather than a joy with too many loopholes.
Vows in Hyrule seem to be taken pretty seriously as well. Link often comes across wayward spirits and cursed people on his travels, trapped because they took an oath that they have yet to fulfill, or they broke one. Based on this, death does not seem to release you from a vow in Hyrule, at least not immediately. So be careful in the wording of any vow you make.
At first, I was going to try and write out individual vows for each Goddess, but after doing a little research and asking Hylia for guidance, I realized that, at best, I can give people a jumping off point. But I can’t really write it for you, because it’s going to be different for everyone. So, below, you’ll find the jumping off pieces I wrote. These are meant to be modified, changed and expanded to fit you, your needs, and your relationship to Hyrule’s goddesses. I hope you guys like them.
Din: “I come before you, Din, Goddess of Power, to dedicate myself to you. When you lift me from my own darkness with your red arms, I will know it is you. When you guard my peace I will know it is you, and when you upheave it to expand my comfort zone I will know it is you. I pledge myself to honor and serve you, and to uphold your virtue within my capabilities.”
Nayru: “Nayru, Goddess of Wisdom, I have chosen this day to dedicate myself to you. Your wisdom knows no bounds and it is you who guides me. When there are truths to behold you reveal them, gently when they are difficult and sternly when I may ignore them. I vow to honor and serve you within my abilities and uphold your virtue.”
Farore: “Dearest Farore, Goddess of Courage, I come before you to dedicate myself to you. You give me courage and hope when I feel lost. You encourage me to step outside my comfort and to improve myself, but also remind me not to be reckless. I vow to serve you and honor you to the best of my abilities, and to uphold your virtue.”
Hylia: “Hylia, her Grace, goddess charged with guarding the Triforce, this day I come to you in dedication. You defended the Surface from Demise and his horde, and guided the Hero. So do you guide and defend me. As you helped the Hero grow and guided him to balance in the virtues of the Golden Goddesses, so you guide me as well. I vow to serve you and honor you within my capabilities, and uphold the virtues of the goddesses.”