How does entropy help decide the spontaneity of a reaction? Consider the endothermic reaction:
$$2\ CH_3COOH\ (l)+(NH_4)_2CO_3\ (s) \to CH_3COONH_4\ (aq)+CO_2\ (g)+H_2O\ (l)$$
This reaction is spontaneous despite being endothermic because the entropy change is sufficiently positive.
I don't understand how the entropy change can effect the spontaneity of a reaction. The molecules are just bumping around, how do they know that the products can occupy more microstates for a given macrostate?
Is the entropy just an complicated way of saying that (due to more microstates) the product molecules are less likely to be in the same neighborhood of each other in order to react and reform the reactants? If so, why not just say that?
At a molecular level, why does higher entropy products lead to spontaneous reactions?
 A: 
Is the entropy just an complicated way of saying that (due to more microstates) the product molecules are less likely to be in the same neighborhood of each other in order to react and reform the reactants? 

No, what you are describing is purely a kinetic effect.

The molecules are just bumping around, how do they know that the products can occupy more microstates for a given macrostate?

They don't.  Entropy doesn't apply at the level of individual molecules. [There are exceptions with very large molecules, but addressing those would require a much higher-level of discussion not appropriate for the OP.]  Rather, it is an emergent statistical property that manifests itself when we have a sufficiently large collection of molecules such that, when we apply a stastistical treatment, the probabilities overwhelmingly favor a single macrostate.
More specifically, the entropy of a system is proportional (through Boltzmann's constant) to the log of the number of possible macroscopically indistinguishable microstates that a system in a given macrostate can sample, weighted by the relative probabilities of those microstates.
As a consequence, if you allow a molecular species additional degrees of freedom (e.g., vibrational), then a collection of those molecules would have many more ways in which they could arrange themselves, giving you a relatitively higher probability of seeing those molecules -- i.e., favoring them entropically.
A rough analogy would be this:
Suppose you have a white ball, a black ball, and three wells.  The white ball can only go in well no 1, while the black ball can go into either well no. 2 or well no. 3 (i.e., the black ball has double the possible ways it can arrange itself). 
Each time you push a button, you allow the balls to go into their wells. Each ball has a 10% chance of making it into a well.  Thus each time you push the button, there is a 10% of a white ball appearing (because it has only one possible configuration) (one well), but a 1-.9^2 = 19% chance of a black ball appearing (because it has two possible configurations) (two wells).  The black ball and white ball have no idea what each other are doing.  Yet, when you consider the system as a whole, you are more likely to see results that have a black ball than results that have a white ball.  Thus the "equilbrium", averaged over many games, favors the black ball.
A: Consider salt dissolving in water. This is an example of a reaction that is endothermic, but still favoured at room temperature. Ions of sodium and chlorine break off of the crystal and dissolve into the water. A sodium ion might be hit by a water molecule and become detached from the salt crystal. In reverse, this looks like a sodium ion colliding with a water molecule and slowing down enough to rejoin the salt crystal. It turns out that it is pretty easy for an ion to leave the crystal, but rejoining it requires the velocities of the particles involved to coincidentally line up just right. This is because there are more states with more salt dissolved in the water, so reaching one with less dissolved salt requires properly aimed velocities. You can think about this like trying to hit a target with an arrow. The smaller the target, the more carefully you need to direct the arrow.
A: According to the formulations in either the laws or the postulates forms of thermodynamics, the entropy change of a chemical reaction is NOT the deciding factor for whether the reaction is or is not spontaneous. The entropy change of the universe during any process determines whether the process is or is not spontaneous. The entropy change of a chemical reaction is only tracking the entropy change of the system. We must also know the entropy change of the surroundings during that chemical reaction.
Translating this to the paradigm of statistical mechanics, we must state that the number of micro states of the reactants or products has no bearing on whether the reaction is spontaneous. The difference between the number of micro states in the products versus reactants will define the entropy change of the chemical reaction. But, that is a system-level result. It tells us nothing about what has happened to the number of possible micro states in the surroundings during the reaction. If that number increases more than the number in the system, then entropy in the universe has increased, and the reaction is spontaneous.
When we want to use a system perspective in our constant (T, p) world, we turn to the Gibbs energy of a process (chemical reaction). This is the deciding factor for whether the process is or is not spontaneous. The Gibbs energy must be negative for spontaneity.
For fun, we could decide to live in a box (system) with constant internal energy and constant volume rather than constant (T, p). In that box, we would only need to track the entropy change of the system to define spontaneity. Such boxes are used for example in theoretical modeling simulations.
