Modulation is the changing of musical keys within one composition. There are a few ways to perform modulation without it failing horribly, but we will be using the dominant chord method.
When modulating, it is best to use keys similar to each other. For example, the key of C major has zero sharps and zero flats, whilst the key of G major has one sharp and zero flats, so C and G major are similar keys. If you know the circle of fifths, you can find similar keys easily (I'll provide some insight onto the circle of fifths later on)
How to perform dominant modulation:
If we are writing in the key of C major, and want to modulate to G major, we do these two steps:
1) Create tension by going to the dominant chord of the key you want to modulate too (So if you want to go from C major to G major, you'd first go to the V chord of G major, which is Dmaj)
2) Resolve the tension on the tonic of the key you want to modulate too (So, in this case you'd go "insert C major chord here" -> Dmaj -> Gmaj)
Here's an example of some modulation, labelled: