In the presence of an applied electric field ($\overrightarrow{E}$) in a metallic conductor

Force acting on an electron in an electric field,
$\overrightarrow{\mathrm{F}} = - \mathrm{e} \overrightarrow{\mathrm{E}}$
where -ve sign represents that force acts opposite to the direction of applied electric field.

The electrons move randomly due to thermal agitation but slowly drift in a direction opposite to $\overrightarrow{E}$ due to the above force.