While many police forensics television shows make microscopes appear complicated, there are plenty of experiments to be done with them that can be very educational. Learning firsthand about the structure of different materials or even parts of living things can be a great way to introduce children to biology or other sciences.
You can examine cells from your own body using a microscope. One example is the cells in your saliva, which you can examine by taking a swab from your cheek. Use a toothpick to wipe the inside of your cheek. Then wipe the toothpick against the slide. Gently smear the slide with the cover slip to thin the layer of saliva. Leave the slide to dry. You can use methylene blue dye to color the cells so they are easier to see through the microscope.
Starches from different sources can be viewed through a microscope. First scrape a halved potato with a knife and place on a slide, covering with a cover slip. The starch cells will be oval shaped or triangular. Compare these cells to the cells from other starches. You can easily view corn starch under a microscope. Rice also contain starch. Soak a few grains of rice before scraping a little bit of a single grain. Mount on a slide and cover. View the differences between the different starches
Viewing insects can be difficult with a microscope. This does not require killing the insect. One insect that can be humanely examined under a microscope is an ant. Catch the ant and place it in a petri dish. Place a small amount of honey in the middle of the dish. The ant will eat the honey instead of madly running around the dish, leaving it open to examination with your microscope.
Flowers are another interesting object to examine through a microscope. Different flowers will have different elements visible. Pansies, for example, have finger-like papillae which give them their velvety texture. These papillae are different sizes in different parts of the flower. At the pistil these are so long they are simply called "hairs." You can remove these hairs and place them on a slide of their own to examine them. Each of these hairs in one single cell, making them ideal to examine.