my connected display screen shows up but I can't get them to work together

My connected display screen shows up with all my files, but I can't get the computer screen and connected display screen to work together.

When the mouse works on the mac I can type, when the mouse works on the connected screen I can open a program or website, but then those only open on the computer. But at that point the mouse is stuck on the display and I can't open any program.

HELP