Acids are neutralised by alkalis and by bases. An alkali is a soluble metal hydroxide, such as sodium hydroxide. A base is a substance that reacts with an acid, for example an insoluble metal hydroxide or a metal oxide. Both make a salt and water: acid + base → salt + water.
Acids are also neutralised by metal carbonates. This reaction makes a salt, water and carbon dioxide gas, which causes fizzing: acid + metal carbonate → salt + water + carbon dioxide. For example, calcium carbonate reacts with hydrochloric acid to make calcium chloride, water and carbon dioxide.
The salt you make depends on two things. The first is the acid used: hydrochloric acid produces chlorides, nitric acid produces nitrates and sulfuric acid produces sulfates. The second is the positive ions in the base, alkali or carbonate. Sodium hydroxide and hydrochloric acid make sodium chloride. Copper oxide and sulfuric acid make copper sulfate.
You can use the charges on common ions to work out a formula. Magnesium ions are Mg2+ and nitrate ions are NO3-. The charges must cancel out, so magnesium nitrate needs two nitrate ions for each magnesium ion. Its formula is Mg(NO3)2.