あるいは

あるいは means "or". It stands between two nouns, or at the head of a second clause, and offers it as an alternative to the first. It is formal: notices, instructions, reports, careful speech.

Between two verbs, each one usually takes か.

あるいは, または or それとも

または means the same and is a little less formal; in most statements the two swap freely. In a question that asks the listener to choose, the word is それとも.

In conversation, a plain か does the job: ばすバスかでんしゃ電車でいけます行けます.

"Perhaps"

At the start of a sentence with かもしれない at the end, あるいは means "perhaps", "it may be that". This is written style; in speech, もしかしたら says the same.