A.
Imagine that clocks have an hour hand, but no minute hand, just a sweep second hand. There's one clock on the wall, with the hour hand pointing to the 12 and the second hand going around.  There's also so old broken clocks lying around (you know they're broken because the second hand isn't moving).  These old broken clocks, however, have the hour hands pointing in different places.
    The clock on the wall corresponds to living things today, and the broken clocks are like fossils, stopped in time.  Now we have the problem of interpreting all this.  What does it mean?
    A scientist makes observations- because the sweep second hand is moving around, perhaps clock hands, even the hour hand, can move and completely change position.  This would explain how these broken clocks have hour hands pointing to different numbers.  Give enough time, something in the movement of the second hand leads to bigger changes that actually move the hour hand.
    You look at me and say, "do you really believe this?  I've seen the second hand go all the way around several times, and there's been no change in the hour hand.  How could the movement of one hand change the position of another hand anyway?"
    "Well," I reply, "we've seen gears, little structures with teeth that mesh together.  Perhaps the movement of one hand can cause the movement of another hand that way.  And if the gears are different sizes, that might explain why we only see one hand moving."  Another problem is that no one has ever been able to open up a clock to actually prove this, and no one ever will.
    The gears, you see, are the forces that change the genetic make-up of populations:  mutations, random drift, natural selection, etc.  And these little changes, over time, bring about big changes such as, in our example, the distinct movement of the hour hand, given all the changes in the sweep second hand (including the passage of sufficient time for it to occur).

B.
    The creatures of the world are well adapted to their environments.  How do we know that?  Because they've been thriving;  they're all here and have been for at least thousands of years.  But if you go back far enough, you see that the world was different.  The movement of the continents, changes in the climate, are all preserved in the rocks.  The information is there:  the Earth has changed.  In that case, the critters that are alive and doing so well today would not have been as well adapted to the environment the way it was.  This leaves you with one clear conclusion: organisms must have changed too.  That history is also in the rocks-  there are fossils of creatures that no longer exist, plus, there are fossils of creatures similar to what exist now but are different.  We understand the mechanisms by which populations change in a short time span-  why could not these mechanisms have produced the big changes we see in the fossils, especially given the long time spans involved?  Evolution provides an explanation for changes in living things over time, based on mechanisms for genetic changes in populations (mutation, drift, natural selection) that we have concrete evidence for,  and observations of geological changes and fossils that we also have evidence for.  Because evolution as we commonly speak of it takes so long to occur, we cannot subject the idea to experimental testing, but all the pieces of the theory work, make sense, and can successfully be used to predict the answers for some experimental questions.