Video: view
Two things are beside each other if they are next to each other, facing the same direction. The two women on the bench are sitting beside each other, or side by side.
By might mean near, as in "she was sitting by the lake".
It might also be used to indicate who did something, for example "this book was written by my brother".
Dis forDown (direction)
Video: view
For means with a purpose of, or intended to belong to. Some examples are:
"I am collecting shells for my sandcastle"
"That cupboard is for the towels"
"Is that for me?"
Not to be confused with four.