As an American, or somebody with a US green card, the process is that you drive up to the border crossing and wait in a line of cars. When it’s your turn at the booth you give them a stack of passports and green cards, let them visually identify everybody in the vehicle, answer some questions, and then they give your documents back and waive you through. It’s basically the same as the immigration process at the airport, except you stay in your vehicle.
Then of course there’s a separate toll booth for your tunnel or bridge.
As an American, or somebody with a US green card, the process is that you drive up to the border crossing and wait in a line of cars. When it’s your turn at the booth you give them a stack of passports and green cards, let them visually identify everybody in the vehicle, answer some questions, and then they give your documents back and waive you through. It’s basically the same as the immigration process at the airport, except you stay in your vehicle.
Then of course there’s a separate toll booth for your tunnel or bridge.
I live in a country with no land borders, so my experience with land borders is only that of a non resident/citizen.