It's very easy to determine the relationship in English.
First, find your common ancestor. Siblings have the same father, cousins have the same grandfather, etc.
- Same grandfather means First cousin.
- Same great-grandfather means second cousin.
- Same great-great-grandfather means third cousin.
If you are not in the same generation, pick the shortest one, then the generation distance is how many times removed.
- Your cousin's child is your first cousin, once-removed.
- That person's child is your first cousin, twice removed.
The labels work the same in both directions so "first cousin, once removed" identifies the relationship to the speaker irrespective of whether that person is in the younger generation or not.