Each creature gets +1/+1 for each other creature on the battlefield that shares at least one creature type with it. (For example, if two Goblin Warriors and a Goblin Shaman are on the battlefield, each gets +2/+2.)
Sharing multiple creature types doesn’t give an additional bonus. Coat of Arms counts creatures, not creature types.
If a creature has more than one creature type, and one of those types matches the creature you are calculating for, then count that creature. Only one type needs to match in order to get counted.
If you have a creature with more than one creature type, count all creatures which have either creature type.