[Nitram2004]

I know that it is something to do with the movement of the molecules and that the more the molecules move the more it dissolves. However, what I don't know is how this happens.

[Krynvel]

Hot water doesn't dissolve more salt than cold water, hot water dissolves salt quicker than cold water.

Think of it this way, you're on a football field and your coach gives you a football and tells you to run it to the end field. There are football players running across the field in random directions, not specifically targeting you but they will hit you if you cross their path. In one scenario the football players are running at full speed. The other scenario are the players jogging at a moderate pace.

In the scenario where they're running each football player has a higher chance of hitting you and knocking you away from the football your holding by virtue of ground coverage per player.

In this example you and the football are the Sodium and Chlorine atom ionic bonded and the football players are the water atoms running (hot) or jogging (cold).

[billnotgatez]

Hmmm I wonder

Hot water doesn't dissolve more salt than cold water, hot water dissolves salt quicker than cold water.
...

From WIKI for Sodium bicarbonate
https://en.wikipedia.org/wiki/Sodium_bicarbonate

Sodium bicarbonate
Solubility in water
69 g/L (0 °C)[2][3]
96 g/L (20 °C)[2][3]
165 g/L (60 °C)[2][3]

For NaCl on sigmaaldrich
https://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma-Aldrich/Product_Information_Sheet/s7653pis.pdf

Maximum solubility of NaCl in water at 25 °C is 357
mg/mL. NaCl is unusual in that its solubility does not
increase appreciably with temperature, since at 100 °C,
the solubility is 384 mg/mL.1
The solubility of NaCl in
water is decreased by adding HCl; it is almost insoluble
in concentrated HCl. The density of a saturated solution
at 25 C is 1.202 g/mL. A saturated solution (23% w/v)
freezes at -20.5 °C (5 °F).1

[Borek]

I know that it is something to do with the movement of the molecules and that the more the molecules move the more it dissolves. However, what I don't know is how this happens.

It is not universal. For most salts their solubility grows up with temperature, but for some it doesn't and for some the change is even negative (lithium sulfate for example).

This is an interplay of several processes - dissolution means destroying crystal lattice (that always requires energy, as molecules or ions in a solid are held together by several types of interactions), hydrating molecules/ions (that always produces energy, question is - does it produce more energy than was required to destroy the solid?) and increasing entropy (when getting from rather ordered solid to freely moving molecules/ions in solution). Effect of each of these processes depends on the temperature. So it is not just a matter of movement of the molecules, it is much more complicated.

[Krynvel]

Won't be the last time I'm wrong 😉. I'm sorry I didn't mean to mislead