There is a whole science to this. Softer water is suitable for lighter pilsner style beers and harder water is suitable for heavier stout style beers. Brewing with pure water is not recommended because a certain amount of three ions (sodium, chloride and sulfate) is generally considered necessary for certain parts of the flavor profile.
If by “pure water” you mean something like distilled water, then there are two answers here. If you are extract brewing, then “pure water” is fine. But if you are brewing an all-grain recipe, then “plain water” is not appropriate.
The ions in the brewing water help set the pH of the wort to an optimal level and can affect the flavor of the beer. In craft brewing, the wort is already done for you, so you can use deionized water. The extract itself will have mineral ions that come from the residue of the malt pulp, and this ion content may be good from a flavor perspective.
The main point is that if you are not comfortable with your tap water, use some sort of filter or buy some water and start brewing.
1) Heat water in your kettle or hot water tank, if you have one
2) Transfer the hot water to your wort tank and add the grains
3) Make sure the grains and water (wort) are well mixed and let it sit for an hour.
4) Heat another 5 gallons of water during the saccharification process
5) Transfer the hot water to your bottling bucket, or, if you bought one, your mulled wine jar
6) Raise the hot water above the saccharification tank to begin the refilling process
7) Collect the sweet wort into your boiling kettle
8) Once complete, boil the wort for one hour.
9) During the whirlpool process, many hot breaks and hops will be removed.
10) Reach the heat exchanger and cool the wort to fermentation temperature