Fast
Used for things with high velocity, like vehicles or animals. It sounds slightly more formal or descriptive than 'rápido'.
Means 'soon', but is often used to mean 'quickly' or 'without delay' when talking about completing an action.
My car is very fast.
Please, don't speak so fast.
The train is very fast/swift.
I need the answer soon/quickly.
'Rápido' is the universal, standard word for 'fast' and is understood everywhere in the Spanish-speaking world.
In very informal, colloquial speech, 'de volada' means 'very quickly'. 'En corto' is also used for 'quickly'.
The slang term 'al toque' is extremely common for something done 'right away' or 'in a flash'.
Informally, people might say something was done 'soplado' (literally 'blown') to mean it was done very fast.
'Rápido' is standard. In very informal contexts, you might hear 'a toda pastilla' or 'pitando', but these are slang.
Forgetting to change the ending for feminine nouns. — 'Rápido' is an adjective and must agree in gender with the noun it describes. For a feminine noun, you must use 'rápida'. For example, 'La chica es rápida' (The girl is fast), not 'La chica es rápido'.
Confusing 'rápido' (fast) with 'pronto' (soon). — 'Rápido' refers to high speed or velocity. 'Pronto' refers to something happening in the near future, without delay. 'Ven rápido' means 'Come with speed'. 'Ven pronto' means 'Come soon'.
Using the false cognate 'fasto'. — The word 'fasto' in Spanish means pomp or splendor and has no relation to speed. The correct word is 'rápido'.