Find a branch. You're looking for something that is going to have the right diameter, depending on the size you like. I'd recommend at least 4 inches.
Cut your branch into approximately 1/2" slices using a saw. To make your slices somewhat consistent, mark your width of your cut by putting a piece of tape on your saw.
To make your base, cut one slice thicker than the coasters – around 2" - 3".
Let your branch slices dry. We put them on a rack for about 2 weeks.
Drill holes in the approximate center of each slice of wood. Try to vary the placement of the holes slightly; they look better when the edges of the stack aren't perfectly aligned.
Sand your wood slices. You can make a simple jig with pieces of wood to hold the slices in place if you're using a sander.
To make the base, drill a hole with the 3/16" drill bit (slightly smaller diameter than your steel rod) in your base piece of wood. Do not go all the way through.
Cut your steel rod to correct length with a hacksaw. Use a hammer to pound the steel rod into the base. The fit should be tight.
Punch out a variety of paper options with your 2" and 1" punches and arrange in pleasing combinations.
Use the small 1/8" punch to make a hole in the approximate center of the paired circles.
Brush Mod Podge onto a wood slice. Place the circles down on top of the wood slices, aligning the holes. Apply Mod Podge on top and let dry.
Apply more Mod Podge, coating the entire surface of the coaster. Let dry.
Let dry thoroughly and then apply a clear polyurethane coating over the top of the Mod Podge to provide a hard finish.