Gas solubility in water tends to INCREASE as the temperature goes down (exactly the opposite is true for most solids). So keeping the bottle in the fridge is a good thing. Keeping it in the back (where it’s colder) is even better if your shelves are large enough to stand it upright (see below for why this is a concern).
The equilibrium point between gas in solution and gas in the “head space” over the liquid is where the chemical potential is the same in both locations. In the gas phase, chemical potential is roughly proportional to partial pressure; in the liquid/solution phase it’s roughly proportional to concentration.
You want the chemical potential to be high in the liquid, which means you need to keep it high in the gas above the liquid. (The “pump” mentioned above actually should be pumping air INTO the bottle; that increases the partial pressures of everything, including the CO2).
If you squeeze the bottle, the theory goes something like this: There is less volume in the gas above the liquid, so the partial pressure will rise more quickly and less CO2 will come out of the solution.
This is correct, but there are other factors involved.
First, the bottle has to hold its shape. If the bottle is trying to go back to the “normal” shape, that’s going to decrease the partial pressure of all gasses in the head space, including the CO2, and MORE CO2 will come out of solution than would otherwise be the case.
Second, you have to assume that the gas will reach equilibrium before the soda goes flat or you open the bottle again. This may or may not be the case.
Personally, I don’t squeeze the bottles, and my wife does. I don’t notice that squeezing has any significant effect either way.
If you’re the only one drinking from the bottle, and you DO (drink straight from the bottle, that is), you might as well blow into the bottle before resealing it. There’s a lot more CO2 in your exhaled breath than there is in normal air (somewhere around 5x as much, I think, but one of our MDs could probably give you a better number).
Leaving the bottle on its side increases the area of the interface between the liquid and the gas. This has no effect on the equilibrium concentration, but it DOES have an effect on how quickly the bottle comes to equilibrium.