You can tell I know nothing about plumbing with that title. So when I turn on the hose, water leaks out of little holes around this gold ring (as in the attached pictures).
Any thoughts on repairing, or how to remove and replace the gold ring?
That gold ring should be threaded onto the faucet. I would say Puddles is right, that is your problem. Remove it by turning it counter clockwise and take it with you to find a new one.
The ring is called a backflow preventer and is just a check valve. If you were to connect your hose to a garden sprayer as many do and then there was a problem in your house or neighborhood requiring pressure to be taken down like a broken pipe or something the water could be sucked back along with the weed killer in your sprayer and get into the house plumbing or the community plumbing. It screws on to the outside valve just like a hose and then the hose screws to it. It is ether bad or isn’t tight or has a bad seal. Some of these have a set screw that holds them in place along with the threads like the hose has. If it doesn’t want to screw off as suggested above look for a little screw on the back side of the ring. Depending on what you use the hose for and what the regulations are where you live you may not need it at all.
You need a pipe wrench to take it off and then you can try to find replacement parts, I filled it up with rubber washers and re-installed it which stopped the leak and then added a screw on backflow preventer which are available anywhere.