"Theodicy" is the word you use to name the act of combining the existence of God with that of evil and pain, in short. That word was coined around the end of the 18th century, and the first notable example of it is John Milton's Paradise Lost.
Justifying the ways of God to Man, as Milton put it in his epic poem, is what theodicy is all about. Surely you have already heard, or thought yourself, that there couldn't possibly be a good or sane God in such a world. In view of all the bad things happening in everyone's life and your own, how could there be a just God leading everything? That's an important question and it is not one that should make you either give up on God or on an explanation.
I will recommend books for that later on, but so far, I will merely attempt to extremely briefly explain how God and evil can coexist. As you have noticed, God doesn't seem to be very present in our every day life. Nor in fact was he very present in the New Testament (excluding Christ, the Holy Spirit, and the likes) compared to the Old one. But that shouldn't be thought of as a proof that there is nothing. Absence of proof is not proof of absence, as they say.
So why is there evil in our God-made world? The short answer is this: because there is freedom, and free will. It would have been easy for God to make a world without pain and evil, but it would have meant controlling us in a very tight way, and ultimately, it would have meant sacrificing our freedom altogether. If you don't have the choice between good and bad, you are not free. Of course, that's quite an expensive freedom. Millions of people have died for it, and all of us suffer for it, but apparently our freedom is worth it. You have the choice between a world where everything works fine, but where no one is free, and a world where all are free, but where those free people will abuse their freedom. God chose the latter, and everyone pays the price, including God himself.
On our scale, this is a bit like teaching your child to walk. If you constantly hold him or her when he or she attempts to walk, the child will never really learn. I suppose any parent knows that sometimes you have to let your child experience things on his or her own. So, when we let our kids walk and fall, that's what God does on His scale when he lets us live free.
Of course, I know what the skeptic would easily say: "That's a simple way to justify His never being around." And of course it may seem so. But think about it. If God had wanted a perfect world, He would have gotten one. However, as I just explained, this "perfect" world would be robotic, and at best a prison. I don't think many of us would be any happy in that. Besides, I don't call that living. It's an act of Love to set us free in such a way, because if anyone has to witness all our pain and suffering, it is God. Moreover, ask yourself if you'd rather live safely in prison or adventurously - and above all freely - wherever you want in the world. The answer is quite easy. Having the choice of your own life, you can even choose a safe way to live it; what matters is that you have the choice, you're free. Evil comes in the game because everyone is free, and not everyone is good. Stupid people are endowed with freedom too, and that causes evil more often than not. That is the price of our freedom.
That was relatively shortish. If someone wants more information on the subject, I strongly recommend reading CS Lewis' theological works (mainly Mere Christianity and The Problem of Pain). Feel free to ask me any question. [Or not.]