Sew all around the placemat 1/8 of an inch from the edge. Take pins out as you sew shut the opening.
Next comes the quilting! You can quilt how every you desire. I wanted to stipple mine (meaning just an overall random quilting). You will need a darning foot. Mine has a metal loop though I know they also come with plastic see through loops. Remember to lower your feed dogs as well so that you are the one moving the placemat around underneath the needle.
* An alternative way to quilt your placemat could be to leave a walking foot on your machine and sew in a rectangular spiral. It gives a different look but also can have a pretty effect.
Here is a glimps of a corner all quilted up.
Here are all 4 placemants that I created for this set. Easy peasy!! Hope you like creating your own placemats. Please let me know if I can make anything more clear for you.