“Toward” is the preferred form in the U.S. “Towards” is favored in the U.K.
“Upward” as an adverb is preferred in the U.S., “upwards” in the U.K. As an adjective preceding a noun, only “upward” is acceptable.
“Forwards,” mercifully, does not exist. Or, as one of my students once said, “fails to exist.”
