How does salt push out the water from vegetables, meat, etc.?
It is called "Osmosis" and the applications of this are many. Since you are a self-identified "noob of chemistry" I'll not go too far into the specifics of why this happens but try to explain on a laymans basis.

As you probably know, water is a solvent. It can dissolve (some) solids so that no solid remains, only liquid. This usually has some effect on the solute (water in this case). Lets say you have two glasses of water - one of which has some salt dissolved in it. Nature would very much prefer if they were at the same concentration of salt. Nature wishes for 2 glasses of water with $\frac{some}{2}$ salt in each.

So, when there is an apple, with water inside and some salt outside, nature would like there to be about the same concentration of salt inside and outside. So she (nature) will provide a driving force for taking water out of the apple and into the salt. The skin of the apple is a semi-permeable membrane: only water can pass. So nature will drive the water through the skin to the salt. And she will keep at it until the apple is so empty of water that it is so hard to find water in the apple that the forces are in balance.

The same thing applies to sugar. Sugar is also one of these compounds that can dissolve in water and will affect the water in the same way.

For a more detailed explanation I'd google "Osmosis". This interesting phenomenon is responsible for many things, wonderful and useful. You can actually pump water with it. Nature will "pull" water against the force of gravity in order to balance out the concentrations. (This is basically how a salt power plant works)