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Galileo began with a telescope. It did not take him long to realize that getting a longer focal length with his telescopes was a big problem. However, using lenses with a shorter focal length, he could, in effect, turn the telescope around and magnify little things. His first microscopes, in 1609, were basically little telescopes with the same two lenses: a bi-convex objective and a bi-concave eyepiece.
The microscope on the left, designed by Galileo, was probably made by Giuseppe Campani.
By 1624, Galileo had developed an occhiolino (the word microscope was not coined by Giovanni Faber until the following year) that had three bi-convex lenses. It did not magnify much more than his telescopes, about 30 times, but Galileo was more interested in the multitude of stars he could see through his telescope than in the insects he examined close-up with his microscope.
The diagram on the right is a screenshot from a terrific online exhibit about Galileo's microscopes, the Museo Galileo in Florence.