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pH

pH goes from 0 (max acidity) to 14 (max alkalinity), 7 is neutral. This is a logarithmic, not a linear scale, so each unit means a change by a factor of 10 in the Hydrogen ion concentration [H⁺]. Tap water in my area has a pH value of around 8. Note pH does not have any units, it is simply a number.
Many freshwater fish come from regions with pH between 6 and 7.5, and will tolerate living in values slightly outside of this. Many livebearers find my tap water ideal, and although tetras and rasboras will live in this water, breeding may involve providing their natural conditions. Chocolate gouramis and parosphromenus species need more acidic water pH 5-6 to thrive. Discus prefer around 6. Rift lake cichlids on the other hand like it alkaline around 8. Seawater has a pH of around 8.
Some fish have been bred commercially in ponds for generations, and may well have adjusted to different values.

What affects pH?

Wood can reduce pH,as may peat extracts and 'black water'tonics. CO₂ addition will reduce pH. Some rocks,stones and gravel, depending on their mineral composition, may well raise it. Those sold in aquarium shops shouldn't to any degree. Decorative items not specifically meant for aquarium use may not only affect the pH, but also be toxic to fish and invertebrates.

Intense light, including afternoon sunshine, on an aquarium may cause an increase in photosynthesis, levels of carbon dioxide/ hydrogen carbonate may decrease, and the pH may rise significantly.

Hardness

Soap is, chemically, the sodium salt of a fatty acid.This will react with calcium ions and precipitate out as 'scum'. You don't see so much of this now, since wash bars, shower gels, shampoos and washing powders are mainly synthetic detergents. Because it was 'hard' to get a lather, calcium-containing water was called 'hard water' and 'hardness' the amount of soap needed before a lather could form.

KH

this is 'carbonate hardness' but can also be seen as buffer capacity, since it binds with acidity, stabilising the water's pH. This one reacts with acids stopping a rapid drop in pH. It used to be called temporary hardness, since it can be removed by boiling. This is the scale deposited in boilers and kettles.
When we measure KH with a test kit, we are measuring the buffer capacity, adding drops until this is exhausted and the pH changes

Ca(HCO₃)₂ --boiling --> CaCO₃ + H₂O + CO₂

GH

standing for 'general' hardness or 'GesamtHärte', this is the total [Ca⁺] and [Mg⁺] in water. Apart from these Calcium and Magnesium ions, there are one or two others present but in such small amounts that we can as aquarists ignore them. The part of total hardness that cannot be removed by boiling has been called 'permanent' hardness.
Tests for GH measure this total amount.

Conductivity

Mentioned in older books but not considered for the home aquarist because of the cost. Nowadays a small digital meter will cost below 30€. Water is a good solvent. On its way to us, it dissolves small amounts of minerals. Some rock formations such as chalk will contain calcium and magnesium, whereas others such as granite and lava will not. The dissolved substances are present as and ions. These electrically charged particles will move in water when a voltage is applied, how much current flows corresponds to the quantity of minerals dissolved. BUT this means all minerals, not just those causing hardness.

Conductivity is measured in microsiemens (µS) . This is the inverse of electrical resistance.

Aquarium water starts off with the same conductivity as tap water. Between 600 and 1000 µS in Berlin. Reverse osmosis water has a conductivity of 10µS. Fish waste, fish food, water conditioners, fertilisers and other additives can change these values. Other things being equal, a significant rise would indicate it's time for your regular water change (max 30%).

Tests

Combi test strips- the least accurate but the most convenient for a quick overview. Stick to well known makes and you'll get 6 or 7 parameters measured all at once. Good value.
Liquid tests- can be selected according to the pH range required. Thes are made of combinations of special dyes called 'indicators' which change colour at particular pH values. Other tests rely on a colour change due to a chemical reaction. Some of the reagents may be caustic or be harmful in other ways. Read the instructions from beginning to end before use.
pH meters- very good but only as accurate as their maintenance and calibration, electrodes do not last for ever. Conductivity meters, very accurate if kept clean.

Terms used:

[H⁺]: Square brackets mean "concentration", here of Hydrogen ions in water, the plus showing this is a positively charged ion. These tend to hang themselves onto water molecules, so you will often see this as [H₃O ⁺].

Other Values

Sorry, not that far yet.

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Water Parameters