1. Count how many generations each person is from that common ancestor.
2. Subtract 1 from the smaller of those numbers to get the "cousin" level
3. The difference between those 2 numbers is the "removed" level
Simplest way to explain, and it is not simple. Take you as the starting person.
Your parent's siblings are your aunts and uncles, and their children are your first cousins.
Your first cousin's children are your first cousins once removed (once removed from you and the main line)
Their children are your first cousins twice removed, and their children are your second cousins once removed.
Going back to your grandparents: Their siblings are your grand (sometimes called great) aunts and uncles, and their children are also your first cousins once removed.
Your first cousins once removed have children and they are your 2nd cousins.
Your second cousins have children and they are your 2nd cousins once removed.
Your 2nd cousins once removed have children and they are your 2nd cousins twice removed.
Back to your great grandparents. Their siblings are your great grand aunts and uncles, and their children are your great grand aunts. Their children are also your first cousins twice removed.
Your first cousins twice removed have children and they are your second cousins once removed.
The further you go back and the wider your tree, the more complicated it gets but the pattern repeats itself and the tree gets wider with each succeeding generation of children.
Most good family tree programmes have line charts showing you the various relationships, and most label each person that you add to your tree with the correct epithet, and have a calculater so that you can work out the relationship between each person on it. .
ie your 4th great grandfather's brother's children were your 1st cousins 5 times removed.
There are also some excellant calculators on line Just put "relationship calculator" in your browser and it will come up with several.
The "removed" means that someone is a generation further (or closer) in in kinship to some common ancestor of you both. "Twice removed" means there are two generations further or closer to the relationship with that common ancestor. So it is that children of your first cousins" sre your "first cousins once removed d" and the kids of those 1st cousins once removed are your first cousins TWICE removed. The word "removed" could be read "generation", OK?.
It's easiest to start with first cousins. As you know, first cousins are the children of sibllings. Second cousins are the children of those children. They are the second generation of cousins. Removed comes into play when stating a relationship across the generations. For example, the first cousins have children. As I said, the children of the first cousins are the second cousins. But, the child of the first cousin is the first cousin once removed to the other first cousin. The relationship is first cousin (because the parent is the first cousin) but the child is one generation removed from first cousin yielding First Cousin Once Removed. I have a Cousin-Finder Sheet that may help you. I have uploaded it for you to see.