How do i know if a health supplement is suitable for vegetarian?

The simplest way to find out is to read the label. According to
American Dietetic Asso, a vegan diet excludes eggs, dairy and
all animal products. So there should not be any of those items or
their derivatives in the supplement you are mulling over.

For instance, glucosamine, which is touted to reduce cartilage wear,
is derived from shellfish such as shrimp, crabs and lobsters.
Even so, there are vegetarian versions, too, like Vitahealth's Vegetarian
Glucosamine Sulphate. Its make from plant sourced glucosamine.