Some examples:

Before I picked my friend up at the airport, I made sure that his plane had arrived.

You will stand before the judge in the trial.

After I picked my friend up at the airport, we went for pizza.

I was the first person in line for tickets; hundreds of people were after me.

I had called my friend beforehand; I knew he was at home.

I picked up my friend at the airport yesterday.  We went for pizza afterwards.

Before and after are prepositions.  Prepositions are only usually meaningful in combination with the noun or phrase which follows them.

Beforehand and afterwards are adverbs. They are complete ideas in themselves and don't need to be followed by anything.