Use a dovetail saw to cut a 1-inch slit down the length of two 1-by-4-inch wooden boards. These boards will serve as the stands for the mirrors.
Cut a circular hole in the center of each acrylic mirror sheet, using a hole saw. Hardware stores can usually do this for you if you do not have a hole saw. If you are using glass mirrors instead of acrylic sheets, use a knife to scrape some of the silver backing off the center of each mirror.
Slide the mirrors into the slits you cut in the wood boards. Set the mirrors about 6 inches apart with the reflective sides facing each other.
Line one of the mirrors with an LED light strand, if desired, to enhance the infinity illusion.
Look through the hole in one of the mirrors to experience the infinity illusion.