Finally means "at the end of a long wait." Although it seemed like it would never end, and in the middle you were cursing the day you signed up for the marathon, when you finally finished, you were overjoyed.
Final means "last," so use the adverb finally to describe an end result or long-awaited satisfaction. Once the tedious dinner party was over, you finally got to go home and watch TV. If you're giving a speech and you have 14 different points that you're going to make, when you get to the last one, say "finally..." and then make the point. You can also say "in conclusion..." if that last point really sums it all up.