Please tell me the correct way to pray at a Shinto shrine.

The basic way to pray at a Shinto shrine is called “two bows, two claps, and one bow” (nihai ni-hakushu ippai).
First, give a slight bow, then place an offering in the offering box.
Next, bow deeply twice, clap your hands twice, and finally bow deeply once more.
It’s important to pray sincerely in front of the deity.