Is scientific knowledge reliable? What does science tell us about God?

The simple answer to the first question is "usually." The hard part, of course, is to know when it is and when it isn't. Unfortunately, we humans lack the omniscience that would let us know which of the findings of science are reliable, and which aren't.

God has revealed Himself to us in several ways. Some of these are:
the Bible
our consciences
the wisdom of godly people
the guidance of the Holy Spirit
the evidence of nature, and especially
Himself, Jesus Christ, the God/man

The bible is clear that God does reveal Himself through the evidence of nature. In other words, through the observations of science. Here are two passages that say that:
Psalm 19:1. The heavens declare the glory of God; and the firmament sheweth his handywork.
2. Day unto day uttereth speech, and night unto night sheweth knowledge.
3. [There is] no speech nor language, [where] their voice is not heard.

and

Romans 1:20. For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse:

(Both of these are KJV, as it is public domain)

So, God can be seen in nature, according to both the Old and the New Testaments.

What does science tell us about God? (In other words, what do we learn about God from observing nature?) Here's a list. It's not complete, and it's tentative:
1) It tells us that God is immense, and extremely powerful.
The sheer size of the universe tells us that.
So does the activity of the sun. It converts about 4 million metric tons of mass into energy per second.
We don't know yet whether there is life on other planets. If there isn't, and the entire universe has only one planet with living things, that doesn't mean that the rest of the universe is, somehow, a waste. God's resources weren't diminished by creating the universe, however and whenever that may have happened.
(We don't know how large the universe is. It may be infinite, or it may merely be very large.)

2) It tells us that God is a God of order and regularity.
Actually, scientific observations, or, for that matter, casual observations, wouldn't be of much use without this regularity. Consider, for example, the periodic table. For another, consider the orbits of the various bodies in the solar system. For yet another, consider yourself. You probably have a few trillion cells. Each of them is descended from a single cell. With few exceptions, all of our cells have the same DNA as the first one.

3) It tells us that God is a God of infinite creative ability.
Estimates of the number of species now alive, or that have ever been alive, are only estimates. Best estimates of the number of species currently in existence on earth are between one and two million. Adding in species which have become extinct, and species yet to be discovered, the number may be as much as ten times that large, or even larger.
As Psalm 104:24 puts it: O LORD, how manifold are thy works! in wisdom hast thou made them all: the earth is full of thy riches.
Apparently, God loves variety.

Science doesn't tell us, but the bible does--the same God, capable of infinite creation, and limitless in power, is concerned about single individual humans, and even birds. (John 3:16, John 4:3-26; Luke 12:6)

Added January 27, 2012: For a more complete treatment of the ways God reveals Himself to us, see here. This post was updated a little on  February 23, 2016. The second part of the title was added at that time. Thanks for reading!