The basic rule is: two people the same number of generations away from a common ancestor are Nth cousins, where N is the number of generations; for people who are not the same number of generations from a common ancestor, they're Nth cousins M times removed where N is the number of generations away from the common ancestor for the one most closely related to that ancestor, and M is the difference in the number of generations removed from the ancestor.
This should go without saying, but you always take the shortest possible chain. Two people who have the same grandfather will also of necessity have the same great-grandfather, but you trace it back to the closest possible ancestor. Also, people with the same parents are siblings, not "zeroth cousins".
A couple of examples:
Two people have the same grandfather. There's one generation between them and their grandfather, so they're first cousins.
Person X is the grandfather of person A and the great-grandfather of person B. Persons A and B are first cousins (one generation between X and A) once removed (1 generation difference in the two chains).
Person Y is the great-great-grandfather of person C and the great-great-great-great-grandfather of person D. Persons C and D are third cousins (three generations between Y and C) twice removed (two generations difference in the chains).
Two people whose grandparents were second cousins (sharing the same great grandparent) are fourth cousins to each other (sharing the same great-great-great-great grandparent).
If two people have grandparents who were siblings, then their parents are first cousins and they are second cousins.People whose grandparents are siblings are second cousins.
If two people are first cousins, the children of one are second cousins to the children of the other.
Two people who share the same great great grandparents are third cousins. To find a cousin relationship, find the common ancestor. If common ancestor is grandparents, they are 1st cousins. If common ancestor is great-grandparents, they are 2nd cousins. If common ancestor is great-great-grandparents, they are 3rd cousins.
There is no law against 2nd cousins getting married.
If two people are first cousins, their children are second cousins. If two people are fifth cousins, their children are sixth cousins.
Two people whose grandparents were second cousins (sharing the same great grandparent) are fourth cousins to each other (sharing the same great-great-great-great grandparent).
It would technically be considered your half- cousin since you do have the same grandmother but a different grandfather.
Any two people are first cousins when one parent of one of the two people is a sibling of a parent of the other of the two people.
If two people have grandparents who were siblings, then their parents are first cousins and they are second cousins.People whose grandparents are siblings are second cousins.
If two people are first cousins, the children of one are second cousins to the children of the other.
Two people who have the same great grandmother are second cousins to each other. Two people who have the same grandparent are first cousins.
Two people who share the same great great grandparents are third cousins. To find a cousin relationship, find the common ancestor. If common ancestor is grandparents, they are 1st cousins. If common ancestor is great-grandparents, they are 2nd cousins. If common ancestor is great-great-grandparents, they are 3rd cousins.
Family trees do not tell you whether people are close or distant cousins; they tell you what kind of cousins people are to each other. You, and the marriage laws in your area, decide whether two people are too closely related to make a family together.
Two people whose great grandparents were siblings are third cousins to each other. The children of siblings are first cousins. The grandchildren of siblings are second cousins to each other. The great grand children of siblings are third cousins to each other.
If two people have the same grandfather, they are siblings or first cousins. If two people have the same great grandfather, they are siblings, first cousins, or second cousins to each other. If two people have the same great great grandfather, they are siblings, first cousins, second cousins, or third cousins.
Two people are first cousins if they are the children of people who are siblings. Two people are second cousins if they are the grandchildren of people who are siblings. Third cousins are the great grandchildren of siblings. It gets more complicated if the two people are members of different generations, but in general people are some sort of cousin to each otherif they have a common ancestor somewhere in their family heritage.