Go walk outside without them on something mildly unpleasant, like "chipseal" pavement or gravel for short distances - the increased feedback will encourage you to walk gently (advice stolen from Barefoot Ken Bob's book, which is rather nice).
Take it slow. Don't feel like you have to go 100% minimal-shoe all the time. Take your shoes off at home. Maybe get a pair of thin sandals - I personally like Xero Shoes (they also sell a kit if you're into that, and they're one of the only pairs of sandal I've had that actually last for multiple years). Moccasins are also lovely, if you can find some with a thick sole (or buy some buffalo hide and DIY!).
Minimal shoes don't last any longer and generally aren't any cheaper than regular shoes in my experience - getting comfortable with your feet on the ground when possible is the cheapest long-term option.
Then just start walking outside. Watch some youtube videos on how to do it and just experiment and adjust the way you walk all the time (to give you a bit of perspective, occasionally I even play around with my walking style today, 2 years after starting). I tried to see it a bit like a stretching exercise in the beginning. If I felt a stretch of tight muscles (usually calves), I assumed that "I did it correctly"; like in stretching, where you only feel a deep stretch if you do it correctly. But important note: This only worked for me because my calves were indeed tight. If this is not the case for you, this analogy won't work for you.
But most importantly, listen to your body(!) and don't be afraid to look stupid in public (experimenting with your way of walking, while learnign a new way walking, will definitely get noticed by others the beginning; at least that was the case for me).
I started with Vibram FiveFingers, but switched to proper barefoot after a short while. If you can do proper barefoot in your area, it's more fun.
Always work barefoot at home, if you don't already do that.