I wanted my future father in law to officiate my wedding ceremony in
Ontario, Canada. How does he go about becoming ordained, can he do so
online, and what are the laws surrounding this in our province of
residence?

The Universal Life Church ordains applicants online.  I was married by
a friend with this credential and it was accepted as legal in Vermont.
Their site has information about where the ordination is accepted as
legal.  Although their ordination is undoubtedly abused, they seem to
be very sincere in their nonsectarian spiritual beliefs.

I checked this (above). The Marriage Act does not recognize the ULC as
a religion, and therefore does not allow ULC Ministers to register to
perform marriages in Ontario. The ULC is working on it, but it's not
an option right now.

This site details one persons quest to become registered in Ontario:

ULC Weddings in Ontario, Canada 
http://www.angelfire.com/ca3/angelgoddessmeditate/ULCinOntarioCanada.html

Marriage Act
http://www.e-laws.gov.on.ca/DBLaws/Statutes/English/90m03_e.htm

This search string should help:
ULC Marriage Ontario "Marriage Act"
://www.google.com/search?num=50&hl=en&lr=&safe=off&q=ULC+Marriage+Ontario+%22Marriage+Act%22

I wonder if the better question is whether a ULC performed marriage in
Ontario is recognized in your home province - not whether it is
recognized in Ontario?