This functionality is built into Windows and Mac OS. You don't need to buy anything for the client.

For Windows you can use Microsoft's Remote Desktop Connection from a Windows or Mac system to connect to the client, the software is free. You can also use one of the third party programs available that allows compatible MS remote connections.

Windows also has a remote assistance feature which should allow the person at the other end to see what you're doing. Normal RDC shuts down the screen on their end.

For Mac OS you can use Apple's Remote Desktop which is commercial but available at a couple of price points I believe. I'm not sure if there are any free third-party programs that can connect directly to the remote service. Can't recal if VNC will do it. Apple's solution has the ability to show or hide the desktop on the client side.

In both OS cases you need to first enable remote connections on the client machine(s).