When a song is played in swing time you will see the marking below next to the tempo:
What this marking is saying is: Whenever you see groups of 8th notes, play them as a eighth note triplets with the second note removed. In the two bars written below, the left side shows standard eighth notes and the right shows swung eighths:
If a piece of music has the swung notation mark, you don't need to write in all the triplets. You will play any eighth notes noted as they are in the left bar as they are written in the second bar. Reducing the amount of triplets used makes the notation much cleaner and easy to read.
Written below is the same four bar piece of music twice, the first example is notated literally and the second uses swing time notation, notice that the second example if far easier to follow and is a much 'cleaner' transcription.
Notice in the second example above that when swung notation is used, eighth notes are always grouped in twos rather than fours. This is to further imply that the rhythm is now triplet based.
When a piece uses swing notation, it is important to remember that any eighth notes are played in the triplet style. It is quite easy to forget about it and end up getting the timings wrong.
To cancel swing time notation the following mark is put above the appropriate area: