Well, I know this is not really practicable, but I will try to cut down a lot of them.
First I use baskets for my shopping by car. They don´t need 200 years to decompose.
The next is to have many fabric shopping bags!... I mean many, approx. 10.
you can left them in every handbag, in every shopping basket, in the car, in the bicycle basket..and so on...
Then, it is great to quit the use of thin plastic bags for vegetables or fruits.
This is possible if I have thin cotton fabric bags. (lots of them)!.
Last thing you have to do is: say NO ! if someone asks : "Do you want a plastic bag" ?