I get this question from time to time and it always bothers me a little. The reason it bothers me is because, in the context of our conversation, the only thing this question could mean is that you are unable to see any answer to that question without seeing the law, even if you don't want to call it that. Let me explain what I mean...
If I were to answer that to love God means to believe His word and to do rightly. Your response would be to say that there is no practical difference between my doctrine and yours. You'd quote John 14:15 and ask how then is what Paul taught any different than what Jesus taught. We would then be at square one and you could reread the whole conversation in answer to that question.
However, despite my previous experiences with this question, I do believe that you're asking the question honestly and so let me give as straight forward an answer as I know how to give....
To love God is like loving anyone else. Asking what it means to love God sounds to me like asking what it means to love your parents or spouse or brother or best friend. It means that God is dear to you, that you value Him and your relationship with Him. And if loved rightly, He isn't simply dear to you, He is your dearest, the One you value above all others.
This, you might think, means that you value righteousness and justice, for to be righteous is to be like God. If you are like the one you love, you'll love yourself and self-esteem is what happiness is.
And you'd be right but Paul teaches us that the doing of it is not achievable....
I am carnal, sold under sin. For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do. If, then, I do what I will not to do, I agree with the law that it is good. But now, it is no longer I who do it, but sin that dwells in me. For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find. For the good that I will to do, I do not do; but the evil I will not to do, that I practice. Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me.
I find then a law, that evil is present with me, the one who wills to do good. For I delight in the law of God according to the inward man. But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members. O wretched man that I am! Who will deliver me from this body of death? I thank God—through Jesus Christ our Lord!
So then, with the mind I myself serve the law of God, but with the flesh the law of sin. (Romans 7)
What then are we to do? We love God and want to do rightly but find that we cannot. Are we then doomed to live out this life in frustration, poor self-esteem and defeat? Certainly not! For if we love God then we trust what He says and He has said that we are righteous, in spite of what we do!
There is therefore now no condemnation to those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit. For the law of the Spirit of life in Christ Jesus has made me free from the law of sin and death. For what the law could not do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, on account of sin: He condemned sin in the flesh, that the righteous requirement of the law might be fulfilled in us who do not walk according to the flesh but according to the Spirit. For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit. For to be carnally minded is death, but to be spiritually minded is life and peace. Because the carnal mind is enmity against God; for it is not subject to the law of God, nor indeed can it be. So then, those who are in the flesh cannot please God.
But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His. And if Christ is in you, the body is dead because of sin, but the Spirit is life because of righteousness. But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you. (Romans 8)
As you therefore have received Christ Jesus the Lord, so walk in Him, rooted and built up in Him and established in the faith, as you have been taught, abounding in it with thanksgiving.
Beware lest anyone cheat you through philosophy and empty deceit, according to the tradition of men, according to the basic principles of the world, and not according to Christ. For in Him dwells all the fullness of the Godhead bodily; and you are complete in Him, who is the head of all principality and power.
In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead. And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross. Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it. (Colossians 2)
Resting in Him,
Clete