Man naturally discovered that when you observe anything through a drop of
water, it appeared larger.
A drop of water is dome-shaped or convex -- wider in the middle and
thinner toward the edges. It is a lens.
As a light ray enters and travels through the drop of water (which is denser
than air), it travels at a slower speed. When this light ray exits back up
out of the drop and hits the air, it bends (refracts) and speeds up. This
bending is what enlarges the image.
In a compound microscope there are two convex lenses (the eyepiece and the
objective lens) working together to greatly magnify the image.
Part of searching for the right microscope is understanding the terminology
and anatomy. Quickly read through the next section and you'll be able to
make the best choice for your needs.