Nothing to Fear But Confusion!
First, it is one thing to have a vague fear about something, as in a premonition of worry, or a number of concerns and worries. Then one can also be afraid of something very specific, like spiders, snakes, rats or closed in spaces.
When referring to a fear as a singular impression at a particular moment and for a specific reason, then the word temor may be used -- in the singular.
Vio que el mar en este lugar era profundo y le sacudió un temor frío (He saw that the sea in that place was deep and a cold fear seized him).
Después de las elecciones, desaparecieron muchos de nuestros temores (After the elections, many of our fears disappeared).
The word miedo is another word, always singular, that refers to fear as an abstraction:
El miedo muchas veces es irrational (Fear is often irrational).
Por miedo, los chicos no quisieron entrar en la casa abandonada (Because of fear, the boys refused to go into the abandoned house).
You can state what someone is afraid of by using the phrase tener miedo de, which is followed by a noun that reveals the cause or source of the fear:
Mis hermanas tienen miedo de las arañas (My sisters are afraid of spiders).
However, if someone is afraid of a person, note that instead of de, the preposition a (personal a) is used:
No tengas miedo a Enrique; en el fondo es cobarde (Don't be afraid of Enrique; deep down, he's a coward).
Finally, the verb temer, related obviously to the noun temor, above, is the verb used to show that someone is fearing something -- which is shown by the object of the verb. It means to fear:
No hay nada que temer sino el miedo mismo (There is nothing to fear but fear itself).
Note in the foregoing example how the object of the verb to fear is the noun for fear that is employed when the fear is an abstraction. It is what FDR would have said if his speech had been in Spanish!