How to disconnect and replace a speedo cable in 1992 Corolla

You will have to remove the instuments. The trim panels are held in by screws and tabs. Be gentle when removing the trim. Then there will be screws holding the instrument panel in, remove them. Look on the tranmison for the speedometer cable connection and remove it and push tha cable into the fireal a bit. Pull on the instrument panel and angle the spedometer side out and feel behind it for cable. It will unscrew with retention cap.
Pull old cable out from firewall and push new one in and connect to speedometer and replace trim. Re-attach cable to transmission.

Any curves on the cable should be kept as gentle as possible. Any sharp bends would shorten the lifespanof the cable. At the meter cluster end it could be the clip on type whereby you need to push a tab to detach the cable.