Affirmative Expressions Negative Expression
algo something, anything nada nothing, not anything
aguien someone, somebody, anyone nadie no one, nobody, not anyone
alguno/-a(s), algún some, any ninguno/-a, ningún no, none, not any
o... o either... or ni... ni neither... nor
siempre always nunca, jamás never, not ever
también also, too tampoco neither, not either

In Spanish, double negatives are totally normal:

Negative statements normally use the pattern no + verb + negative word. When the negative word precedes the verb, no is not used:

Once a negative word is used, all other elements must be negative if possible: