The one removed, twice removed stuff can be very confusing, but it is actually quite simple.
For example, take a couple and call them generation 1.
Their children, generation 2, are siblings.
Their children, generation 3, are first cousins (same grandparents).
Their children, generation 4, are second cousins because you have to go to their great-grandparents to have an ancestor in common.
Their children. generation 5, are third cousins because you are another step away from the common ancestor.
Now, a cousin from generation 4 is related to someone from generation 3 'once removed' because of the different in relationship to the common ancestor (great-grandparent vs grandparent). In a similar way, generation 5 is 'twice removed' compared to generation 3.
However, the more generations you go, the more confusing it can get. And, when there are several marriages within the family tree (e.g. two sisters marry two brothers, and their great-grandchildren end up married, joining the two lines), that is how that you can end up being your own ? cousin x times removed.
Hope this helps clear things up.