How would you explain/support that in geology "the present is the key to the past"?

Theologians and natural philosophers in Hutton's time believed that Earth was less than six thousand years old, based on the Anglo-Irish prelate James Ussher's mid-seventeenth-century calculations. Geology was also influenced by the charismatic German mineralogist Abraham Werner, who contended that most rocks were sediments deposited during the biblical Flood, and who dismissed active processes like river erosion and volcanism as recent and insignificant phenomena. While Werner regarded Earth as remaining static until the next divine catastrophe, Hutton saw it as dynamic, preferring to consult "God's books"--the rocks themselves--rather than the Bible for insights into the history of the planet.

Hutton's theory of the earth was published as a paper by the Royal Society in 1788 and then in book form in 1795. Unfortunately, he was such a poor writer that few read his book. We owe Hutton's legacy to his friend John Playfair, whose 1802 Illustrations of the Huttonian Theory of the Earth made the ideas accessible and appealing. It was not until the 1830s, however, when Charles Lyell published Principles of Geology, that geologists were generally ready to accept and implement Hutton's approach and to move from biblical interpretations of Earth's physiography to those based on observation, experimentation, and reasoning.

After two hundred years, Hutton's principle of uniformity is still at the heart of geology. Scientists recently observed, for example, copper sulfide and zinc sulfide being deposited on the seafloor by scalding fluids jetting out of hydrothermal vents (see "Neptune's Furnace" page 42). This find led to a reinterpretation of the 2.8-billion-year-old copper and zinc ores of Timmins, Ontario, and linked them to ancient seafloor processes.

I would interpret this as follows:

We can see geological processes taking place i.e. vulcanism, sedimentation, erosion. One basic assumption of scientific theory is that laws governing behaviour apply universally - i.e. there is nothing particularly special about this particular time or this particular place. Therefore if we see erosion of a certain type of rock taking place at rate R today, we will make an assumption that this rate is was the same in the past.

well, we can't travel back in time, so we have to look at the present evidence to make theories about the past.