If the initial velocity is zero then it will keep it that way.
If the initial velocity is in the same direction of the magnetic field, then the electron will move with constant velocity.
The force on the electron in the magnetic field is $\vec{F}=q\vec{v}\times\vec{B}$.
If the direction of $vec{v}$ is parallel to direction of $\vec{B}$, then $vec{F}=0$.
so it will move with constant velocity.

If the direction of $vec{v}$ is perpendicular to the magnetic field $\vec{B}$, then the force is also perpendicular to the velocity, so the force will only  change the direction of velocity -- and it is a circular motion.

If velocity contain both parallel component and normal component, it will move with helical path.

You are welcomed to check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=36.0]Charged particle motion in E/B Field[/url].