The way I visualize orientations of $1$- and $2$-dimensional objects is by an ant walking along a path. For a $1$d object (like a line/ line segment/ etc), just place the ant on the line and confine it to walk in only one direction. Then it only has two choices as to the direction it walks -- those are the two orientations. For a $2$d object (like a plane/ planar triangle/ etc), place the ant inside the object and then confine it to walk in a circle. It can either walk in a clockwise or counterclockwise circle -- those are the two orientations.
How can I similarly (or completely differently) visualize orientations of $3$d objects?