1. Expect to hear God's voice.
Jesus says: "The man who enters by the gate is the shepherd of his sheep... his sheep follow him because they know his voice. ... I am the good shepherd; I know my sheep and my sheep know me". [John 10:2,4,14]
In other words, Jesus tells us that we who follow him will know his voice. If you assume that Jesus isn't talking to you, then you won't hear him. He says he IS talking to you; how could he expect you to recognize his voice if he never talked to you? The first step to hearing him is to try believing that he is, in fact, talking to you.
Set aside time, preferably every day, to silence your own thoughts. Give him a chance to speak. If someone I know holds their hands over their ears and hums something while I'm trying to talk to them, I usually respect their choice and stop talking; if they don't want to hear, yelling isn't going to do any good. God is the same way; he doesn't yell at us if we don't want to hear. If we don't be quiet and listen for him, he's not going to shout over the noise that fills our minds.
3. Ask questions.
This goes along with God not yelling at us if we don't want to hear. He doesn't necessarily answer questions you don't ask. So ask what you want to know. In my experience, he doesn't answer all the hypothetical "what if ..." questions that run through my head, nor does he answer questions about what's going on with other people. But he almost always answers the "what should I do right this moment" questions, the ones that are based in reality instead of in my imagination.
4. God speaks in your heart.
Eldredge goes on (and on) about the heart, in his book. One important distinction that he makes that I think especially worth pointing out is that the Biblical idea of the heart is not the sappy idea that our culture has of the heart being our emotions (and thus opposed to our head, with which we think). In the Bible, we think and know with our heart; our heart absorbs wisdom (Luke 5:22, Deut 8:5, Eph 1:18, Prov 23:15 for example). Eldredge says emotions can be a sign of what is in our hearts, (I believe he uses the phrase "the voice of our hearts") but they are not themselves our hearts. Our heart is the center of our being. Personally, I found it useful to stop expecting God's voice to be one of the many voices running through my head, but to be something deeper.
Don't expect yourself to just suddenly start hearing him perfectly someday. Like most things in life, hearing God is something that needs to be practiced and learnt over time. This insight was one of the two most helpful to me. Without realizing it, I was expecting there to be some magic, logical key which would clearly identify thoughts from God from other thoughts; once I got that key, I would be able to know exactly what God was telling me and what he wasn't. The idea that hearing God was something I had to learn, like you learn how to ride a bike or how to read a book, was something I needed to hear. You can hear God clearly one day and the next day still struggle, just as one minute you can be on the bike going forward and the next minute you fall off again. But over time, things improve if you keep working at it.
6. God never speaks harshly.
This is the other insight that was most helpful to me. While God does, in fact, tell me things I don't want to hear, including pointing out my sins to me and insisting I stop them, there is always a gentle sternness when he does this. All those harsh thoughts - the ones you can identify because, if you listen, their tone is screaming "you're a lousy piece of shit", even if the words are just "you forgot to do the dishes" - none of those are from God. And, if you haven't done it already, you cannot believe what a relief it is to really accept fully that those words are from Satan and that God really doesn't think that about you, even if he did want you to do the dishes.
7. God never contradicts what you know.
Of course, sometimes you need to be careful about mistaking your assumptions for what you really know. But this is still a helpful thing to keep in mind. There really are some things we can know, and God doesn't contradict these. Eldredge isn't Catholic, but for those of us who are, Catholic doctrine should be included in with other things that we know as guidelines that help us discern what is or is not God's voice.
8. Acquire wisdom and test revelations.
Eldredge breaks up God's voice into two broad categories: wisdom (which in this context, broadly speaking, means God tells us something by revealing that we already know it in our hearts) and revelation (which, again broadly speaking, means God reveals something new and specific to us). He says the best way to acquire wisdom is through pouring over the Scriptures. One example (I believe he calls it "eerie"; I would be less equivocating in my quotes, but I leant the book out to a friend) he gave of revelation in his own life was when he was flying to England or Ireland to give a retreat, and God told him to schedule his flight a day earlier than he had planned. He found out why only afterwards, when the attacks on Sept 11, 2001 caused all flights to be grounded, including the one he would have taken. There was no wisdom on Eldredge's part that could have told him to fly a day earlier - God simply revealed it to him.
Along these lines, Eldredge says that when we receive a revelation, especially if it seems to contradict wisdom, it should be tested repeatedly. By testing, I think he means that we ask God again and again and see if we are getting the same answer (as Gideon does with the fleece in Judges 6). He might mean more than that; I'm not sure yet.
9. Obey God.
This goes along with #5, "Practice". Actually doing what you think he is telling you to do and seeing the results - good or bad - can give you a better idea of what he sounds like (and doesn't sound like). But also, I say this because even if you could hear God crystal clear, it would do you no good if you didn't actually do what he tells you to do.
10. God's voice brings peace.
This was first said to me - at least so that it stuck - not by Eldredge, but by a member of my Monday night Charismatic prayer group. Sometimes - all too often, really - what God tells me is something where my first inner response is resistance, irritation, or anger. But if I relax that tensing up, I find a sense of peace wherever God's will lies. If I am resolved to do something that is not God's will, then (if I pay close attention to my inner self) no matter how much I try to relax, there remains a sense of irritation or unsettled-ness. This is one of the single most reliable marks of God's voice that I have found.
UPDATE: Further thoughts at Walking with God, Part II. (5-20-09)