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Even if your design is small, it would still be a good idea to do this. This way, you will be able to keep the rest of your mat clean while you paint. If you have a larger design, you may need to print it out onto several sheets of paper. Alternatively, you can also sketch your design onto the back of your contact paper freehanded or using a stencil. Make sure that your design is big enough to that it is proportionate to the mat. If you drew your design directly onto the back of the contact paper, you can skip this step. Place your contact paper onto a cutting mat with the stencil facing upward. Use a craft knife to cut through both the printed paper and contact paper. Remove any pieces of tape and regular paper that might still be stuck to the contact paper stencil when you are done. If you do not own a cutting mat, you can use a sheet of cardboard instead. Contact paper is not very sticky, so it likely won't stick to your doormat very well. In this case, you can secure it with sewing pins. Simply poke the pins straight through the contact paper and into the mat. Focus on the areas that have a lot of detail. Some people find that spraying the back of the contact paper will also help it stick.
Cut a sheet of contact paper so that it is a few inches bigger than your doormat. Print your design out onto a sheet of paper. Tape your printed design to the contact paper. Cut the design out using a craft knife or Xacto blade. Peel the backing off of the contact paper, and press the stencil onto your doormat.