To find instances of a term in a document with vim, use the following while in command mode:

/term-to-search-for

Then n and shift+n may be used to navigate forward and backward through all occurrences of this term.

This will not count the total number of instances of the term, however, and for that there is a simple option, also used while in command mode:

:%s/product//gn

Resulting in:

8 matches on 8 lines

This has returned the total count for this search by using the substitute command, which here is not replacing the search term, but rather is counting the number of matches with n, and allowing multiple matches per line with g.