I originally posted the simple silhouettes I did of my kids, pictured below, but didn't provide pictures of the steps, and since the offspring have been asking why I haven't done one of Vince, I decided to make everyone happy, and provide pics of just how easy this is.
Take a picture of your subject...here's the fine specimen, our dog Vince...
Print this picture on plain paper
Use a glue stick to temporarily attach it to black construction paper, then cut out the picture. I cut the picture first, but you can skip that step and cut them together. Take your time, every little ridge shows. I purposely cut around his lash because it looks cute.
Remove the original, and use flat black spray paint to "darken" the construction paper. It gives it a "velvety" look, makes it look old. Don't saturate it, just a light spray.
(You could probably use black cardstock and skip this step, but I didn't have any on hand.)
Glue the finished product onto white or cream cardstock and frame it.
Now I guess I have to do the cat.