Search for "Through-Hole Soldering" on this How To Solder guide to ensure you replace and solder the LED correctly.

Align your new replacement LED in the correct location.

Pull the wires on each side of the new LED through the holes in the circuit where the LED was previously.

Solder its joints in the back. Be sure the soldering joints create a concave tent shape indicating a strong connection.

Use a tool such as tweezers to hold the new LED in place so that your hands are not near the hot soldering iron.