That's a complex question, but it's the same as knowing what sort of fittings to use where when plumbing or wiring a house, or what sort of paint, stain, varnish etc to use when refinishing furniture. It starts with having knowledge of the various types of components, their pros, cons and characteristics. Then you have to know what purpose you wish the capacitor to serve. Physical characteristics and price take consideration and are some rules of thumb and intuition involved too. Like any form of engineering, it relies on many layers of knowledge.

For a really basic overview, electrolytic capacitors are used where large values are needed at low cost, like for filtering the outputs of power supplies, longer duration timing and low frequency filters. Small ceramic capacitors with their very low ESR are used for decoupling and high frequency timing and filter circuits. Tantalum and multilayer ceramic capacitors provide high capacitance, extremely low ESR, very compact size and very long life in the same sort of applications that electrolytic types would normally fill. There are of course MANY other types of capacitors out there, but this covers some of the most common.