The only thing that determines if a gene change is "successful" is survival. Take a group of brown rabbits in a snowy environment. A genetic mutation (random) occurs in two rabbits, one is born with bright white fur and the other bright red. The white one is well camoflauged and thus more likely to survive. That rabbit then is more likely to reproduce white offspring with the white gene. The bright red rabbit would stand out and likely be eaten, thus no new generation to inheret the red gene.
I just gave an example above that shows a beneficial example. Of course most mutations would be harmful because there are far more ways to disrupt a system than improve upon it. What do you mean exactly by showing steps between species? A frog will never turn into a dog so there will never be something in between. Even assuming you are talking about two "species" on the same genetic line, let's say homo habilus and homosapiens, the "step" in between would be homo erectus. The word 'step' is a little misleading because there are an infinite number of 'steps' just as there are infinite color steps between orange and yellow.
What happens? You might get a different trait (e.g., hair color, eye color, etc). They aren't copies as in the exact same genetic code. You have 23 pairs of chromosomes. Each pair is made up of one from your mother and one from your father. Unless your mom and dad have the exact same DNA (highly unlikely), your chromosome pairs will not be identical to eachother.