Very few items are needed to make a distressed sign - the base material wood in this example, paint primer, paint and sandpaper
once you selected your base material do not send it smooth, just carve the image, clean it up if needed and and apply paint primer on it.
Once primer is dry paint it with a paint of your choice I use oil based paint but latex or acrylic paint will work too.
Let is dry for 24 hours at the room temperature
Lightly sand the surface with a 120 GRT sandpaper trying to distress the desired area.
Once you achieve the wanted effect you can apply a protective finish like a clear lacquer or a polyurethane
Keep in mind that some finishing products will change the color, for example polyurethane add an amber hue.