It works the same as in quantum electrodynamics. There, if you have some configuration of charged particles (e.g. electrons and protons), they will be emitting and absorbing virtual photons, or causing excitations of modes of the electromagnetic field - in a quantum field theory, virtual particles and field mode excitations are just two ways of talking about the same thing - and saying that a point in space has a certain density of virtual photons, or a certain average level of field activity, gives you the electric and/or magnetic field strengths at that point, and therefore also gives you the force that will be experienced by a charged object at that point.
In a string model of physics, a photon will correspond to a particular type of string, like an open string with both ends attached to a particular brane; and for another type of string to count as electromagnetically charged, it has to be capable of emitting the photon type of string. So that could be an open string with one end attached to the "electromagnetism brane", and the other end attached to a different brane, like the "electron flavor brane". That would be an electron type of string, and if the end of that string attached to the "electromagnetism brane" budded off a new string which was attached at both ends to the "electromagnetism brane", that would be an electron-string emitting a photon-string.
Once you have that, everything works as before. The electron-string stretches between the electromagnetism brane and the electron flavor brane, and its electrostatic field is a density of virtual photon-strings that it produces in the electromagnetism brane, and which emanate from the point where the electron-string is attached. In fact, the photon-strings actually are quantized vibrations of the electromagnetism brane. The brane's vibrations are described by the Born-Infeld equation, which is an old modification of electrodynamics that long predates string theory, and which reduces to Maxwell's equations at low energies.