I think there are two sources of confusion here:
- How potential surfaces relate to forces.
- How work is defined on a potential surface
You are talking about an electric potential but all potential surfaces work in the following way:
The (negative) gradient of the potential surface is the force acting on the particle. So, in an equipotential (flat) surface, particles feel no force (the gradient is zero everywhere). No force $\implies$ no acceleration but particles will continue their trajectory if they start with some initial momentum. So particles can (and do) move without work being done.
Now there is an easier way to calculate work done if you know the start and end points of the particle trajectory on the potential surface: work done is merely the difference between the potential at the start and end points (the potential difference, or when dealing with electric fields, the voltage). This can be calculated without any knowledge of the path the particle took between these two points.
Now lets link everything together. A particle is at rest in an equipotential. You decide to move it to another point. You accelerate it, allow it to continue for a while and then decelerate it to rest. How is this compatible with the above two paragraphs?
- By accelerating the particle, you apply a force. You can't have a force without a potential gradient so the particle is no longer in an equipotential, it is in a downward sloping potential. You do work on the particle during this stage.
- When it stops accelerating, it is once again in an equipotential and moves at constant speed.
- As the particle begins to be decelerated, it is again, no longer in an equipotential. This time the slope is positive. The work done initially is given back to you exactly. The particle returns to rest at a different point in space.
- The particle sits happily in an equipotential at a different point to before. No work has been done as all energy given to the particle has been recovered.