You will need a flashlight, small adjustable wrench, rags, and a small container to catch water with. Remove all the items stored in the cabinet under the sink so you can get in there and work also a small amount of water may spill so the items should be removed to prevent them from getting wet. You do not need to turn off the water to the faucet but the faucet cannot be turned on while the sprayer and hose it being replaced. There will be a small amount of water in the hose, which will leak out when it gets disconnected.
Trace the hose under the sink from the sprayer back to the bottom of the faucet where it connects. Unscrew the hose connection using the adjustable wrench or, in the case of the newer quick connect hoses look at the new hose to see how the quick connect operates and then disconnect it. Place the end in the container to catch any water in the hose and wipe up any spilled water with the rag. Go back up topside and operate the nozzle to allow air into the hose draining any water still in the hose into the container then pull the hose out through the top. Insert the new hose down through from the top and put the sprayer in place. Go back under the sink and either screw the replacement hose connector onto the connection and tighten or, snap the quick connect in place and lock it.
Go back up top and turn on the faucet operating the sprayer leave it running and go below again to check for leaks. Run the faucet to get the water coming out as hot as possible and spray the hot water through the hose then with the hot water in the hose shut the faucet off go back below to remove any coils so the hose hangs straight. The hot water will aid in getting the memory coils that were in the hose from being stored in the bag out of the hose so that it pulls out and stores again without tangling. Clean up under the sink and put the items that were stored in the cabinet back in place. Enjoy your brand new side sprayer.