We call the seats the passenger seats and the driver's seat.
The right side of the car is usually called the passenger side of the car.
I "get comfortable for my drive" — for my commute — notice we use drive there as a noun; it can be a verb and a noun.
"I put my coffee mug into the cup holder."
A mug, "mug," is just a big cup.
We talk about coffee mugs, they're big cups that you put your coffee into.
In many cars, there is a special place for a cup or a bottle, and that's called a cup holder, "holder."
It holds the cup so you can have your coffee in your car.
I "put the keys in the ignition."
The keys are, of course, what starts your car.
It's the piece of metal that you open your car door with — you unlock it.