Function: intransitive verb
1 : to be dependent
2 : to have confidence based on experience
I rely on the merits of him who is mighty save. And when I say "rely" I mean so in a highly specialized way. After a number of pioneers had been rescued from the harsh winter conditions of the unforgiving American plains, Brigham young told the already established saints that all the prayers and faith in the world wouldn't help the suffering (much), they didn't need prayers they needed potatoes and other temporal necessities, or something to that effect. As the saying goes God helps those who help themselves and in select cases others intervene on God's behalf in the lives of those who try to live right by him. In this world most stuff is up to humans.
When we say we rely on God, it's not the same as saying that I'm relying on Joe Blogs to pay me today that 20 bucks he owes me from last week, I think what we're saying, when we're on top of our game anyway, is that I'm going to do what I think is right, and God gave me this sense of distinguishing between right and wrong, so hopefully this decision and action will help me on my way back to him. In other words reliance on God doesn't place the responsibility for our destiny on his shoulders, we're not the US Congress handing our powers all over to the Executive branch, in crisis we need to take responsibility for our own bailout. I have a feeling that God interferes in human affairs as little as possible, partly because so little has been seen of him lately or even ever. It is safe to say that we can expect few Deus Ex Machina moments. He put the wheels in motion, and now he's watching them turn making minor adjustments as needed, any major adjustments need to be handled by us. In the gospel rely=DIY.
note: this post is talking about life in a temporal sense, reliance obviously extends into the eternities with the effects of the atonement etc.