EDIT This answer is wrong, because of my incorrect assumption regarding the reasonability of extending scattering theory to the classical world, (I think?), but there is a related post: Scattering and Forces, which addresses a similiar question
From that post:
In quantum field theories, because locality, forces are always produced by interactions, i.e. correlations made by virtual particle exchange, or field fluctuations if you prefer. So, a repulsion between particles are actually a probabilistic phenomena. The probability of two electrons be close together decreases as they get close. This is so because they have a probability to exchange virtual photons that affects the probability of each particle, producing this kind of correlation. Everything in quantum mechanics are probabilistic phenomena.
Also from this post: The Escape of Particles from a Black Hole
A particle is an excitation of a field, not the field itself. In QED, if you set up a static central charge, and leave it there a very long time, it sets up a field $E=kqr^2$. No photons. When another charge enters that region, it feels that force. Now, that second charge will scatter and accelerate, and there, you will have a e−−>e−+γ reaction due to that acceleration, (classically, the waves created by having a disturbance in the EM field) but you will not have a photon exchange with the central charge, at least not until it feels the field set up by our first charge, which will happen at some later time.
Obviously, I am trying to support my very naïve and loose answer with quotes from those with greater experience in QFT than I have, in the hope of improving it.
Have a look at this diagram, which shows the interaction (repulsion) between two electrons.
Please don't read the straight lines of the electron as indicating that a definite trajectory is being followed, it's more of a schematic that anything realistic.
Image source: Wikipedia: Møller scattering
On the smallest possible scale, this is how a "force" is transmitted between two particles.
The word scattering refers to the fact that the electrons have an influence on each other, what we would call a push or pull (force) in Newtonian mechanics.
Reading through this: QED might help you follow how forces are dealt with on a microscopic scale.
Because its quantum mechanics, we can't use the Newtonian $F=ma$, as this is only applicable to macroscopic objects with definite positions and trajectories.
Instead, we calculate the probabilities that a certain amount of momentum will be transferred between the electrons.
This calculation takes into account the chances of any electron being in a particular place at a particular time and the chances of a photon being emitted and absorbed to, in effect, transfer momentum between the electrons.
But once you see the word momentum, its not difficult to think as linking back to Newtonian forces for a large group of particles.
That's what we do when we return to the classical world, where the probabilities of finding a larger object like a soccer ball at some place (or following some trajectory) other that where Newton laws say it should be are so small that we can ignore them and use $F=ma$.