Prepositions of Movement

Prepositions are used to show movement to or from a place.

For example:-

to, through, across

We use to to show movement with the aim of a specific destination.

For example:-
I moved to Germany in 1998.  
He's gone to the shops.

We use through to show movement from one side of an enclosed space to the other.    

For example:
The train went through the tunnel.

We use across to show movement from one side of a surface or line to another.

For example:
She swam across the river.

More prepositions of movement
She ran...  
  across the road. (from one side to the other)
  along the road. (The length of the road.)
  around the playground.
  away from the policeman.
  back to the shop.
  down the hill.
  into the room.
  off the stage.
  onto (on to) the platform.
  out of the theatre.
  over the bridge. (from one side of an open space to the other)
  past the opening.
  round the track.
  through the tunnel.
  to the door.
  towards the bus stop.
  under the shelter.
  up the hill.

At and in can also be used as prepositions of movement, but they're used to show the purpose of the movement.

For example:

I threw the paper in the bin.
Let's have dinner at my place.

When used after some verbs, the preposition at also shows the target of an action:

The bowler was sent off for throwing the ball at the umpire, instead of to the batsman.

!Note - a lot of sites say that around and round are the same, but there can be a difference, especially in BrE. If someone says "they were running around", it implies the movement is erratic.

For example: Children tend to run around at school.

In BrE when we use "round" we imply a more definite purpose and a more circular movement.

For example: The athlete ran round the track.