By fluid we mean non-solid, essentially liquid or gas. One
definition of a fluid could be something that a solid can move
with a vanishing driving force in the limit of vanishing speed.
Thus by its very definition a fluid does not produce a drag
force for v=0. On the other hand when v increases we know from
experience that a force must be applied to maintain the motion
and hence the drag force appears with increasing speed.
As for kinetic friction the drag force is always
directly opposed to the velocity vector. Experiments
show that to a reasonable approximation the drag force follows the
expression
is the density of the fluid . For air at the surface of the earth
we have 
. A is the area of the solid as seen
in projection along the direction of motion, and 
is a dimensionless
constant which varies from 0.1-1 and depends on the fluid as well as the
solid. v is the speed of the solid in the fluid.
Thus we get large drag force when an object with large cross sectional area
moves at high velocities in a dense fluid. The constant
must be measured: it is a phenomenological parameter which is
difficult to calculate from first principles.