I went by my car or I went by car?

I've found a fantastic post about it on Happy English website so I copy-paste it here:

Preposition Lesson: In the train Vs. on the train

Today we will keep moving ahead with prepositions by going over some more specific items and those which are often confusing.
Travelling
We can go somewhere by car, by train, by subway, by plane, by helicopter, by boat, or by ship. However, if we decide to walk then we go on foot:

• Fred was going to come to my house by bike, but since he got a flat tire, he is coming on foot.

Caution! I have heard some students say, “I went by my car” or “I came by walk.” This is not correct. You walked. And, if you go on foot, we know it is your feet, so please do not say “my.” It’s the same with “by car”:

• I went there on foot. Not: I went there on my foot or I went there by walk.
• I drove there by car. Not: I drove there by my car.

Let’s get ready to leave

• Before travelling, we get in the car, but we get on the bus, get on the train, and get on the plane
• After travelling, we get out of the car, but we get off the bus, get off the train, and get off the plane
• You also get on your bicycle, get on your bike, and get on your motorcycle.
• When you are finished you get off your bicycle, get off your bike, and get off your motorcycle.
• If you travel on foot, you put on your shoes, and then take them off when you want to relax

Where are you?
You can be on the train or in the train. Here is the subtle difference:

• I’m on the train. (I want you to know how I am travelling and I am travelling by train)
• I’m in the train (I want you to know my location and I am inside the train)

The same pattern above works for the bus, train, plane, etc…except for the car:

• I am in the car. If you say, I am on the car, it means you are on top of the car!

Well, I hope this was helpful. If you need me, I’ll be on the train….How do you get to work?