Anytime you install a new floor, you have scraps. I put down some laminate recently and was thinking of what I could make from the scraps before they got tossed out. Always short on coasters because of my prolific beverage consumption habits, I decided to make a couple to match my floors for the top of my bar.
Laminate floorboard scraps
Quarter round scraps
Some sort of clamp
Step 1: Gather Your Scrap
For these I used some left over "Uniclic" flooring with attached padding I had put down in my living room as well as some quarter round I had left over from doing the trim work around my fireplace... both sort of a cherry oak color.
Step 2: Cutting the Frame Pieces
Take the quarter round and cut a 45deg angle off one of the ends. Hold that piece up against one of your scrap floorboard pieces with the inside of your 45deg angle against the outside perimeter of the floorboard and mark it on the opposite side of the floorboard. Make your mark so that the piece will be cut ever so slightly shorter than the floorboard is wide... it's easy to trim down the floorboard later but if you make this piece too wide you won't be able to adjust it later.
Once you've made your mark, cut at a 45deg angle opposing your previous cut. Now you'll have a short piece of quarter round with a 45deg angle on each side, the insides of which will be close to the width of a floorboard. Now take a scrap little piece of wood and lay your little piece of quarter round down with the saw blade up against it and clamp the scrap behind the quarter round so that you can cut as many pieces as you need identically. Once you cut the number of pieces you need (four per coaster) at this length, flip the operation around and cut the 45 off of their other side... duplicating your first piece.
Step 3: Assembling the Frame
Lay your quarter round pieces out in groups of four. Push them together like a picture frame, if you did an accurate job in the last step everything should line up pretty clean without any gaps at the joints. Take a bit of quick setting "crazy" glue (cyanoacrylate for the nerds) and apply it to each end of each piece. You don't need much, just a bit, but put some on each end to make sure you're getting a good bond. If all your pieces and cuts are straight you should just be able to push the whole thing together by making a diamond with your hand and pressing equally on all sides of the square. You only need to hold it together for a minute or two while the glue sets. After you let go let it sit another 10 minutes or so to dry further, and have a beer.
Step 4: Cutting Out the Bottom
Measure the width of one of the assembled frames. If you've done everything correctly up till this point it shouldn't matter which direction you measure in, the length will be the same. Do this to check for squareness. Now go to your saw and measure the same width between the outside tooth of your saw blade and a scrap piece of wood. Get that dialed in and clamp the scrap piece down tightly, so that you can make multiple cuts against it.
Take the scrap floorboard you have and cut it down by butting it up against the scrap... cutting off the tongue and groove material on either side first and then one more cut to square it up. Now drop a piece down into your frame. It should fit without forcing but also be fairly snug. Adjust your saw setup and go at it again if it's not pretty close to perfect. You don't want gaps for glue to seep through in the next step.
Now repeat until you have enough bottoms to fill your frames.
Step 5: Putting the Bottoms on Your Coasters
You can see from the photo that this floorboard came with padding already adhered to the bottom. This actually works out pretty good, it gives a bit of a non-marring non-slip base for your coaster. If you have this you might want to do as I did and have that spongy material sticking every so slightly above the bottom of your coaster. Flip your frames upside down and create shims so that when your bottom is put in upside down, the foam sticks up just slightly above the rim of the frame as shown in the side view photo. Now, put a bead of wood glue around the perimeter of the frames bottom and brush it into the crevice so that it's not all globbed up and doesn't leak down onto the face of your coaster. Let it all dry out, at least a few hours on the wood glue or until it isn't tacky at all, then put it down somewhere and make a beverage to sit on it and enjoy. (Yes there is ice in this whiskey, cut me some slack my soapstones were all used and warm and I like my whiskey cold)