I use 100% cotton fabric and batting. Make sure to prewash all fabric before hand, this means that once they are finished the placemats are machine washable. And really let's be honest here, placemats should always be machine washable.
You will need:
1 yard of fabric of the for the top of the placemat
1 yard coordinating facric for the back
rotary cutter/cutting surface
needles and thread
Step 1: Cut Top, Back and Battling:
Cut the fabric you wish to be the top side- I cut my 12"x16" but measure a placemat whose size feels right for you and go with that. The size you cut the top will more or less be the end size of the placemat.
Lay the top piece on top of battling and cut around the edge so your battling is the same size as the top piece. The battling has a sticky quality so you most likely not need pins. Also if you are a tab short of battling in one place you can tug a bit, battling is very forgiving stuff. (note if you lay the top fabric print side up when you are cutting the battling you don't have to separate and realign these later)
Step 2: The Sandwich
The battling and top are already nicely stuck to each other now lay the top and battling on top of the back with the wrong side of the backing facing up: you will then have back fabric (wrong side up), battling, top fabric (right side up). Place the battling and top piece roughly in the center of the back fabric. Now if you need to you can get out a ruler and do this just so but I eye ball it and it seems to work okay.
Step 3: Pin
Place pins through all three layers all over so that it doesn't shift when quilting.
Step 4: Quilt
Take a deep breath this isn't that scary, promise. This is a great way to get the hang of small quilting by machine. You can trace a pattern or make straight lines. I do meandering thing myself not really straight with a bit of curve to it. **Make sure to back stitch at the beginning and end. I usually sew to from on edge to the other and instead of breaking the thread stitch down an inch or so and start the next line of stitches in the other direction.
Step 5: Edge
Roll the edge over and pin.
Again, due to late night project time I didn't do mitered corners. I simple rolled the next side over and pinned it down.
Step 6: Sew Edge
If you are on a sewing machine roll by all means sew down the edge with the machine. I like to slip stitch the edge in place. I really can't tell you why I prefer this but I do.
So there you have it: placemats. Simple, fairly easy and machine washable. This is a great weekend project even for a beginner.