What’s the relationship between our obedience to God’s word on the one hand, and God’s grace in saving us on the other?
Many people would answer this question very simply along these lines: "Salvation is a reward for obedience. Do the right thing, and God will look after you." It shouldn't be hard to see the problem with that kind of thinking, which (thankfully) is not very common, at least among Christians.
Another misunderstanding, however, is more common among us. It goes along these lines: "Salvation is an act of God’s grace, and then God then calls us to do 'our bit', namely, to obey his word. God gives us Christ, and then he tells us to pull our socks up and start following him."
Again, this is a misunderstanding, but it's important to see why. The truth is found in Psalm 119:146: "I call to you; save me, that I may observe your testimonies."
Notice the logic here (expressed by a regular waw conjunction in Hebrew, but no less clear in this context than the English "that" or even "so that"): The Psalmist pleads for God to "Save me", anticipating that as a result of this he will be able to "observe your testimonies."
In other words, to walk in God’s ways is neither an attempt to earn God's favour, nor is it "our part" of a divine-human transaction whereby, having been saved, we attempt to stay on the right side of God in order to keep him happy. Rather, a life of faithful obedience is itself a gift from God. It's the best way to live, and is itself part of the blessing of being saved. Obedience to the word of God is not "the price we pay" to stay in the good books of the Almighty; it is an aspect of his kindness to us in Christ.