The dashboard light that illuminates the speedometer needs to be replaced. There s no guidance in the manuel.
how to replace adashboard light on 2001 Toyota Corolla
If you can still see the speedometer well enough at night, you may want to delay repairing this. If you decide to fix it now, you will need to have a mechanic (probably at the dealer) replace the bulb. They will have to take the dash apart to get to the bulbs, so consider having all the bulbs replaced at one time. I just had this done on my 2000 Taurus. Four lights were out (I was loosing a bulb every 4 - 6 weeks as they burned out) and I opted to replace all of them. Only cost me around $100.