In golf who shoots first on each hole?

Answer 1

Initially it is random by toss of a coin or something similar. From then on whoever wins the hole plays the next hole first. Whilst on a fairway whoever is furthest from the green plays first.

On the green whoever is furthest from the hole plays first. However is one player has very short 'tap in' then they can be given the 'honour' so as not to interfere with the other player(s).

This is a general rule and local rules may alter this.

Answer 2

The players tee off the first hole in order of lowest to highest handicap. From the second hole, the player with the lowest score on the previous hole has the honour and it continues like so.