The other computer isn't under Nearby
Same network, not guest Wi-Fi or a VPN? On Windows, allow the firewall and set the network to Private. On a Mac, allow Annex under Local Network. Or use Connect by Code or Address….
It's listed but greyed out
It isn't sharing yet: turn on sharing on that computer.
Extend Display is greyed out
A sharing Windows PC needs the Extend-mode display driver, an option in its installer.
Black screen when viewing a Mac
Allow Screen Recording for Annex in System Settings → Privacy & Security, then turn sharing off and on.
The mouse and keyboard do nothing
The sharing computer must allow your device under Paired Devices (and a Mac needs Accessibility). Turn on Control the other computer on yours.
The PIN keeps failing
After 5 wrong PINs, pairing pauses for 10 minutes. Type the PIN shown on the sharing computer.
The picture lags
Use a cable or Direct Wi-Fi, or set Quality to Fast (Wi-Fi).