across vs through: Across = from one side to the other on a surface (across the road, across the river). Through = entering and exiting something (through the tunnel, through the forest).
into vs onto: Into = entering an enclosed space. Onto = moving to a surface above (climbed onto the roof).
out of vs off: Out of = leaving an enclosed space. Off = leaving a surface (she fell off the bike).
along vs across: Along = parallel to the length (along the river). Across = perpendicular, from one side to the other.