I have a client who is a blogger in the US she is using a independent contractor in Canada. Does she issue her a 1099 at the end of the year or how does she handle the payments to this person?

If she paid $600 or more in that year, and she deducts such expenses on her own taxes, then yes.
(Technically the answer is a flat yes if 600+)

You question is hard to understand. There are 3 people Client, blogger, IC in Canada. Who is supposed to get the 1099, the blogger or the IC in Canada? Does Canada use a 1099? That is a US IRS form.

NO Forms 1099-MISC are generated for contractors working outside of the United States UNLESS they are U.S. citizens.