1. By using a conjunction:

Time: and, before, after, while, when
Reason, cause or consequence: and, because, so that, so……that, such a ……that
contrast: but, although

I called her back so that I could confirm one or two details.
The consignment was delivered while we were very busy.
The goods were repacked so quickly that we had no time to inspect them.

2. By using a linking adverbial phrase (often starting a new sentence):

Time: Before that, After that, And then, During this time
Reason, cause or consequence: Because of this, This is why, As a result, Consequently
Contrast: Nevertheless, However

I wanted to confirm one or two details. That is way I called her back.
The consignment was delivered on Friday. During this time we were very busy.
The goods were repacked at once. Consequently there was no time to inspect them.

3. By using a preposition:

Time: before, after, during
Reason, cause or consequence: because of, due to
Contrast: in spite of

I called her back because of the need to confirm one or two details.
The consignment was delivered during a very busy time.
Due to our prompt repacking procedure, the goods were not inspected.