This is usually achieved with sandpaper after painting. Chalk paint is a great choice for this technique. Here's a link for you:
This information may help:
Here are some more ways
You can also do this with stain, take a look here:
Over paint or Stain and when completely dry, rub down areas to show the original colour through in places.
Hi Shelly, hope this video is what you are needing to make your furniture look distressed.
I like to use semi gloss paint when distressing furniture because it doesn't absorb stain or wax asMore
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One tip to add to the above, use a sanding block rather than sandpaper. It is easier to hold and makes the job so much easier.