How does the Earth know when to send a graviton to a newly born particle? Pardon if this is a silly queston, but I'm reading this for the first time. It says that the force we perceive between two objects is an effect of the exchange of the force carrier particles. Even though gravitons are never detected, I thought of considering the idea that gravity works by exchanging gravitons.
Suppose a new particle is born from the decay of some heavy particle or from pure energy or teleported from another universe!? I get that the particle and the Earth don't feel gravity instantaneously. They both need to exchange the force carrier particles. Assuming the graviton travels at light speed, does it take some finite time before gravity is felt by the particle ? I guess so. But the question that is troubling me is how does the earth even know that a new particle is born so that it needs to initiate sending a graviton to the newly born particle?
 A: I'm afraid the account you've read is very misleading, though it's just one of many such misleading accounts. Sadly the popular science press frequently mislead in this way.
If we quantise gravity using the usual quantum field theory approach then we get a particle called the graviton. Roughly speaking the graviton is the quantum of the gravitational wave i.e. when a gravitational wave is created or absorbed this process involved the creation and absorption of gravitons. These gravitons are real particles that carry energy and momentum and they can in principle be detected, though in practice they are so hard to detect that it's unlikely it will ever be achieved.
But, and this is the key point to understand, these real gravitons are not involved in the gravitational force. When two particles experience a gravitational attraction it is not being caused by these real gravitons.
So what is actually going on?
When we quantise gravity we promote the classical gravitational field to a quantum field. This field exists everywhere in spacetime and it can carry energy and momentum, and in particular it can exchange energy and momentum with any particle that has mass. It is this exchange that is responsible for the gravitational force. The problem is that the equations that describe the interaction with the field are too hard to solve exactly so we have to resort to an approximation called perturbation theory. Specifically, we describe the interaction as if it was due to virtual gravitons and we calculate the strength of the interaction by considering all the ways these virtual gravitons can exchange energy and momentum.
But, but, but ...
These virtual gravitons do not exist - that's why we use the description virtual. They are a computational trick we use to get around the difficulty of the equations. The gravitational force is not due to swarms of virtual gravitons flying to and fro between the interacting masses. If we ever manage to construct a theory of quantum gravity that does not rely on an approximate perturbative approach then that theory won't have virtual gravitons and future generations of popular science writers will have to find some other way to mislead the public.
In your example the newly created particle can immediately start interacting with the gravity quantum field because the quantum field exists everywhere in spacetime i.e. in all of space and throughout all of time. The particle doesn't have to wait for some other mass to spot it's there and start flinging it gravitons.
A: The underlying framework of nature, as far as we have discovered and modeled, is quantum mechanical, and the exchange of particles is part of the quantum mechanical modeling.
In quantum mechanics one works with wave functions to compute the probability of an interaction happening, in your case a new particle appearing in the interaction. Your question could be rephrased as :" how does the proton scattering on a proton at the LHC know when to create a Higgs" . Knowledge at the particle level is contained in the mathematical models that have successfully described the particle physics data up to now.
The gravitational interaction is usually ignored, and when calculating the potential interactions between incoming particles to see what is the probability of getting the new particle, the equations take into account the electromagnetic, or weak, or strong potentials , as the  gravitational one is very very small in comparison. 10^-33 of the weak force.
If one can compute at such accuracy, and if the effective quantization of gravity is assumed, then one should include the gravitational potential in the calculation of the wave functions which will give the probability of the new particle appearing. There would be diagrams with a graviton exchange.
So the answer is that the gravitational field of the earth will exchange a virtual graviton with the newly generated particle, increasing exponentially the complexity when thinking in terms of feynman diagrams and exchange particles.
It is not necessary to go into this detail because of the very small effect of gravity at the particle level. Only in very special experiments quantum mechanics enters in gravitational interactions:

The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei. In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory

