Hi, I am trying to fix my kitchen sink sprayer. I have seen a lot of videos concerning that and decided the problem could be from the diverter. The problem is all of the videos I saw look nothing like mine. So when I try to open the top cover inorder to get to the diverter it won't budge! I don't know if I am doing it wrong or if the thing has never been opened before.
The kitchen sink looks like the picture on this web page.. .
A New Retro Sink and Dishmaster Faucet Are Installed in Mom’s 1950s Time Capsule Condo | No Pattern Required

The very top should unthread counterclockwise. If you can't get it to break loose, you can try tapping all around the outside lightly with a hammer to help jar it enough to be able to unthread it with either a pipe wrench, strap wrench, or channel locks (my tool of choice in this case, but know you may scar the surface). Trust me, you can get it off, but damage to the unit may result if you aren't careful. Take your time, use sufficient force, and you should be able to get it done. If not, just imagine how nice a brand new kitchen sink faucet would look.

Thanks, I didn't have all of the tools you mentioned so I used instead a wrench to loosen it, and guess what?. I didn't just scar the surface, I made it smooth! I just left it alone until I can buy the tools I need. Or I will just leave it to someone who knows what they are doing. :) but thanks for the help.

At this point, a new faucet will be your best bet.