The best way to change the covers on a baseboard heater is to begin by finding covers that are compatible the heater before removing the old covers. Make sure the power to the room is turned off when working on electric baseboard heaters.
For electric baseboard heaters, unscrew or unsnap the cover. This might take some investigation as well as trial-and-error due to the wide range of styles that baseboard heaters come in. If the heater is hydronic (one that uses water), cut the screws from behind the heater to detach it from the wall. Do this with extreme caution as it is very easy to damage the heater, the wall or a person in the process.
Once the cover is removed, applying the new cover will just be a matter of doing the process in reverse, replacing screws or snapping the replacement cover into place.
Every baseboard heater has its own design and its own peculiarities. Some of the newer models have covers that snap away, while most older models are screwed or riveted into place.