Down
We usedownmostly as a preposition or adverb. It means ‘in or moving to a low or lower position or level’:
We randownthe hill like two little children.
Jamie, put that vasedown! You’ll break it!
We can also usedownto mean ‘towards the south’, ‘generally in the south’, or ‘towards the place where a river meets the sea’:
When you were living in Spain, did you ever godownto Granada?
We went on a cruisedownthe Nile for seven days. It was fantastic.
In informal situations, we can usedownto talk about a quick trip to a destination which we consider to be less central than where we are. In this meaning, we can use it with or withoutto. Withouttois less formal:
I’m just goingdown (to)the shop. Do you want anything?
Are you goingdown (to)the golf club tonight?
Downcan also mean ‘along’. We can use it withfrom:
Mila’s office is justdownthe corridor, second door on the left.
They live justdownthe streetfromour house.
A good dictionary will tell you more meanings ofdown, especially when it is used as part of a phrasal verb.
Downwards,downward
Downwardsis an adverb. It means ‘movement towards a lower position’:
The garden slopes gentlydownwardsin the direction of the river.
Could you point the reading lampdownwards? It’s shining in my eyes.
In American English,downward(with no final-s) is used as an adverb:
Since the nineteen seventies, our country has really taken some stepsdownward.
In British English,downward(with no final-s) is normally only used as an adjective:
The statistics for violent crimes have shown adownwardtrend in the last two years.(The numbers have gone down.)