Short in the Primary Coil
One of the first things to check for is a short in the primary coil. If the insulation has become scratched or worn away, metal from the start of the coil could be touching metal near the end, causing the effective number of loops in the primary coil to be fewer than normal. The ratio of the voltage in the secondary coil to the voltage in the primary is equal to the ratio of the number of loops in the secondary to the number of loops in the primary. Therefore, if there are fewer loops in the primary, then the ratio of loops is higher, and the voltage in the secondary coil will also be higher. You can test for a short circuit with an ordinary multimeter.
Testing
As an example, consider a transformer that is supposed to produce 24 volts in the secondary coil. If your multimeter says that it is instead producing 48 volts, switch the multimeter to read current. If the current is half of what it is supposed to be, then the power in the secondary coil, which is equal to the voltage multiplied by the current, is still the same level as the power supplied by the primary coil. This is a clue that neither the power supply nor any element in the primary circuit is at fault. As another example, if your 24-volt transformer is producing 36 volts, a current reading of two-thirds of what it is supposed to be, then there may be a short in your primary coil. In this case, you need to either replace the primary coil or, if this is impractical, replace the whole transformer. In general, suspect a short circuit if you read a current in the secondary coil that is equal to 24 divided by the voltage actually produced by the secondary coil multiplied by the current that the secondary coil is supposed to produce.
Power Supply Problem
If, on the other hand, the current is not equal to this value, then suspect a different problem. For example, if your 24-volt transformer is producing 48 volts instead but the current remains at the value that it is supposed to be when the transformer is functioning properly, then you have twice as much power in the secondary coil as is theoretically being supplied by the primary coil. Transformers do not create power out of nothing. Your transformer is likely just fine. Instead, something is wrong with your power supply, which is sending too much power. In this case, you do not need to repair or replace the transformer.
Other Circuit Elements
It is also possible that the problem lies in neither the power supply nor the transformer. If the voltage reads high but the current does not indicate a short circuit in the primary coil, then check the other components in the primary coil circuit. A short elsewhere could cause a drop in resistance in the whole primary circuit. This in turn will cause more of the voltage in that circuit to drop across the primary coil. This increases the power to the secondary coil and, in turn, the voltage. In this case, you do not have to repair or replace the transformer, but you do need to check the other circuit elements with a multimeter.