In evolution, does the change in animals happen during their lifetime or do their children come out changed? (Just asking, my science teacher isn't really helpful)
Well, the change that happens during a person's lifetime typically can't be inherited, so isn't relevant to evolution. There are a series of mutations in each of us (~150 or so) that are not in our parents, but this, too, isn't really a good description of evolution. This is just the source of the variation upon which evolution acts.
Evolution acts on the the level of species. The idea is simply thus: imagine we have 50% of the population with trait X, and 50% of the population with trait Y (this could be a different color of hair, height, whatever). For whatever reason, people with trait X are more likely to successfully reproduce. This means they are either more likely to survive, or are better at attracting the opposite sex, or whatever. Either way, on average, those with trait X have more children.
Thus, the next generation, since the people with gene X had more children, they make up a larger percentage of the population. If this pressure remains for a few generations, soon nearly every member of the population will have trait X, and trait Y will be rare.
Eventually, one of the hundreds of mutations that occur in each of us might lead to a trait Z of the same type as X and Y. This trait might disappear because it's no good. Or it might stick around and not do much of anything. Or it might make people with this trait more likely to survive, making the descendants with this trait Z come to dominate the population after a number of generations.
Or, conversely, the selective pressures might change, and suddenly people with trait Y start having more children than those with trait X (or Z). Then the population switches back: trait Y comes to dominate.
Anyway, that's a very, very basic view. If you want to know more in detail, I highly recommend UC Berkeley's evolution site:
http://evolution.berkeley.edu/
It's quite understandable, and they provide a good rough overview of how evolution occurs, and why we are so confident that it does, indeed, occur.