How to remove faucet spray hose
It's hard to tell from the picture but there should be three copper tubing extensions coming down from the faucet under the sink. Two are water supply lines - hot and cold - and the other supplies the water to the sprayer. Sometimes these hose are attached to the copper extensions by quick-connect clips sometimes by threaded connections. It appears that yours are threaded. Be sure to turn off the water to both the hot and cold supply lines before disconnecting anything.
You should be able to remove the lines from the copper extensions with a couple of properly sized open-end or adjustable wrenches. The threaded nuts will turn in a counter-clockwise direction (lefty loosey - righty tighty). Hold one wrench on the copper nut and the other on the chrome piece with the flat sides. Turn the chrome nut counter-clockwise when looking up. After you get them off you should be able to slide the ring over all three copper extensions - that's why they are staggered with different lengths. You may also need to remove the weight on the sprayer hose if you have one. They usually just unclip with a little pressure.