How much work must be done on an electron to accelerate it from rest to a speed?

You haven't provided a final speed, therefore, I cannot provide a specific answer.
However, I will try to help you out.

Work can be considered as the change in kinetic energy. Therefore, the amount of work needed can be calculated by getting the difference between the final energy and the initial one.

Final energy = α * m * c²
where:
α =  where v is the final speed reached

Initial energy = m * c²

The difference between the two will simply be the answer you want

Hope this helps :)