Who governs the rules of golf globally?

The Rules of Golf are determined and administered by two bodies, (i) The Royal and Ancient Golf Club of St. Andrews (R&A) who govern all territories except for the USA and Mexico and (ii) the United States Golf Association (USGA).

Details about the Rules of Golf

On the inside of the R&A rule book is a basic principle that guides all of us each time we step on the course, "Play the ball as it lies, play the course as you find it, and if you cannot do either, do what is fair."
The two bodies together publish the rules every 4 years.
As the game evolved different clubs found themselves with their own variations of the rules. You can see some fascinating detail via the USGA link below.
The R&A undertook a major revision of the rules in 1891 established the R&A Code that was soon widely followed.
The USGA was formed in 1894. They adopted the R&A Code but allowed themselves the option of modification.
With two bodies there were still two sets of rules. Finally, on January 1, 1952, the golfing community world wide played from the one set of rules as the R&A and USGA issued their first unified code.
Read the earliest surviving written rules of golf, dated 1744. Rule 12 of the 13 gets in the way of today’s Ready Golf!
If you’re interested in the evolution of the rules of golf this summary on the USGA site is excellent.