Across is a preposition. It describes the relationship between two persons, places, or things. It is sometimes used with the preposition from.
Example: That house is across the street.
Cross is most commonly a verb or noun. As a verb, it means "to go or place across." As a noun, it means "an object made of two intersecting segments."
Crossed is the past tense or past participle of the verb to cross.
Examples: Will you cross the street with me? (Verb)
Jesus, Peter, and Andrew each died on a cross. (Noun)
He crossed the street with me. (Past tense)
Their trademark is a pair of crossed swords. (Past participle)
Cross can sometimes be an adjective meaning "opposing," "placed across," or "angry."
Examples: They were working at cross purposes.
He was counting the cross ties on the track.
Please don't look so cross.
Across occasionally is used as an adverb.
Example: She ran across to say hello.
Do not use acrossed, crossed, or acrost as a preposition or adverb.
(The words acrossed and acrost are strictly nonstandard. They are sometimes used by writers to show dialect.)
Incorrect: He stared acrossed the aisle at me.
Correct: He stared across the aisle at me.