What force creates ions out of neutral atoms? Consider the reaction between Na and Cl to form NaCl.
Na loses an electron and "gives" it to Cl because this makes both atoms more stable. 
But what forces "pulls" the electron from Na to Cl? Both atoms are electrically neutral at the beginning, so the electron that is going to be transferred isn't acted on by electrostatic forces.
Since its not electrostatic forces that pull the electron from Na to Cl (since both atoms are neutral) what force pulls the electron from Na to Cl to make both atoms more stable?
 A: Your interpretation that if we have simply an $Na$ atom and a $Cl$ atom they would exchange electrons and make $NaCl$, is wrong !
To make the necessary electron exchange they need to get very very close, so close that their electronic orbitals (place where electrons reside) overlap in after coming into this region 2 things can happen


*

*The electron that is to be shared hangs somewhere in the middle of both atoms; This is known as a covalent bond usually formed between atoms of similar electronegativities. 

*The electron that is to be shared shifts too much towards one atom; This is known as ionic bond usually formed between atoms of different electronegativities.


Now collisions between atoms are constantly made, sometimes the atoms repel due to different orientation of their induced dipoles and sometimes attract, even when their orientation is right they come so close only when they have sufficient energy known as activation energy.
Another point of discussion is that when electrons are in such a close vicinity what causes the exchange from one atom to another.  
In short, Z-effective this is the net charge of the neucleus felt by the electrons at different locations of the atom. Z-effective of a more electronegative is more even on the outer section of atom and hence an electron feels more attracted towards a more electronegative atom. This is what happens in case of $NaCl$, when the atoms come too close the electron migrates from $Na$ to $Cl$ due to the difference in electronegativities of the atoms. 
A: It isn't correct to think of the electron as a little ball that is plucked from the sodium atom and thrown into the chlorine atom. The electrons in atoms don't have a defined position. Instead the electrons occupy a region of space centred on the atom, with the probability of finding the electron decreasing with distance but in principle extending to infinity.
So if you have a sodium atom and a chlorine atom in close proximity (but still farther away than the NaCl bond length) there is a small but non-zero probability of finding the $3s$ sodium electron within the chlorine atom. You don't have to move the electron to the chlorine atom because there is a finite probability that is already there!
If you could watch as the two atoms were brought together you'd see their electron atmospheres start to overlap, and as they did so the interaction between them would increase the electron density near the chlorine atom and decrease it near the sodium atom. However all that is changing is the probability of finding the various electrons, and this increases gradually. There is no sudden transition where an electron pops off the sodium atom and onto the chlorine atom.
A: The stronger positive nucleus of one atom firstly pulls the electron(s) of the other atom. This makes one atom positively charged and one negatively charged causing an ionic bond to be formed
