Could you please tell me how Quantum field Theory describes the attraction and repulsion of two charge particles via exchanging photon?
This is truly hard to visualize from a classical/semiclassical point of view. Having said that though, let me try to explain it from a nontechnical point of view which is generally presented most of the time. Think of you and your friend are standing facing each other, a certain distance apart, throwing a football back and forth. Every time you catch the ball thrown by your friend you receive a small force pushing you backward because of the conservation of linear momentum. You would experience the same effect when you throw the ball and this repeated throwing and catching push you further apart. Instead of standing on the ground if you conduct the experiment standing on two small boats on water, the effect will be more vivid. Clearly you can connect this to the repulsion of two particles by exchanging photons.
On the other hand, visualizing attraction is a bit more tricky but, this time think of the same situation where you and your friend are facing away each other and both of you are skilled frisbee throwers. Your friend can throw the frisbee and curve it in such a way that you catch it from your front. Unlike the previous case, both of you now experience a force that brings you close to each other (A boomerang might be a better tool).
Originally this was a question that came under the realm of quantum field theory. The whole notion of attraction and repulsion of charged particles is attributed to the exchange of virtual photons. Unfortunately this very notion makes it more confusing and hard to understand. But, before we proceed, let us try to understand the common quantum version. Electric field of an electron, compacted in a small region of space creates a virtual (off the mass shell) photon out of uncertainty principle. This virtual photon propagates and reaches the other electron conveying the action and transferred momentum. So, why are they called ‘virtual’? Or, how are they different from real particles? The reality is that these virtual particles are not at all particles but are disturbances in the field. Electrons or positrons (same as electrons with a positive charge) are real particles, a small ripple in the electromagnetic field. Virtual particles, on the contrary, are disturbances that can not be created on their own and have to be the result of real particles or fields interacting with each other. In fact, virtual particles are not particles at all and are kind of a mathematical trick to simplify a complex problem. (In a more mathematical sense, real particles are solutions of wave functions whereas "virtual particles" are associated with the Green’s function.)
So, what happens when two charged particles come close to each other? Let us consider an electron is approaching another electron. Being a charged particle, electron disturbs the electromagnetic field around it and this disturbance reaches the other electron carrying all necessary information (energy and momentum). It is important to note that this disturbance is not a particle and can be exactly quantified if we have enough information about the interacting electrons. This very disturbance is the cause of repulsion between the two electrons. In case of an electron and a positron (two oppositely charged particles) this very disturbance is responsible for the attraction although, this time it is different from the previous one in nature. In quantum field theory, these processes are presented through some diagrams (tools for calculation rather than the picture of original phenomena) called Feynman diagrams which contains all the information necessary to calculate these effects.