The biggest water issue most new brewers have trouble understanding is the difference between pH and alkalinity. Basically, pH is a measure of how far along the scale (measuring Hydrogen ions) something is, alkalinity is a measure of how strongly it resists moving along the scale.
Think of it like a tug-of-war: how far from centre the rope/tag has been moved is like the measure of pH. Could we easily move it back the other way? If it was a 40lb child on each end, an adult could easily shift the rope. If there was a group of 10 280lb man mountains on each end, we would need more effort to shift the rope. That's like alkalinity - how much resistance is there holding the rope (or pH) in place. Bicarbonate wants to hold the pH higher than we want it. That's why it all needs to be removed for brewing, by countering it with acid (acid-base neutralisation).
Alkalinity can be removed by direct addition of acid, or using acidic grains (dark grains are acidic). Pale grains (most base malts) are also slightly alkaline, compared to target mash pH. Target mash pH is typically 5.4, but most pale grains are about 5.7 (but variable). Therefore, the alkalinity from pale grains also needs to be countered. The good news is that brewing water software does a reasonable job of getting you in the pH range you need for brewing (some will argue that point, but few brewers make their own calculations of pH) simply by entering the grains you are using and your water profile. I'd suggest you give mash made easy a try - it's simple and developed by a brewer on this forum (Larry, aka silverismoney) who'll assist when needed.
What else do you need?
Chlorine, or chloramine where used, needs to be removed because it can make beer taste bad. Simple. Add a campden tablet to your water and leave it overnight. I use rainwater so this isn't an issue for me and I've never had to do it.
Calcium: You need some to help several brewing processes, including yeast flocculation. Most sources say 40 to 50ppm minimum. I've brewed with 20 to 30ppm and the beer was fine.
Magnesium: You don't need to add any.
Sodium/Chloride/Sulfate: These affect flavour, just like different types of seasonings in cooking. Sodium can increase flavour perception. Chloride pushes the malty fullness of beer. Sulfate lends a dryness that suits bitter beers. You can try adding very small amounts to a glass of beer to see how they affect flavour perception.
Hope this helps!