I think the example code you posted would convert to this (in theory):
func _process(delta):
self.position.x = get_global_mouse_position().x
I have not tested the code above, so I cannot guarantee it will work. (Unfortunately I’ve had little time to test/work with Godot today :neutral:)
The biggest change from Godot 2 to Godot 3 that I’ve found is the removal of getter/setter functions. Most of the times, any function that has set_ or get_ generally can be used by simply using the variable name. Another change is any short hand, like pos, has changed to its full name, position.
Let us know if you need any help, and good luck!